LIBRARY OF CONGRESS. 
QB#5~ 

Sjpji* ©jjpjrigJfi 3§u* 

Shelf 



UNITED STATES OF AMERICA. 



ASTRONOMY. 



Science gttamrate. 



ASTKONOMT. 



W. H. MfgHRTSTIE, M.A. F.R.A.S., 

Astronomer Royal, Greenwich Observatory. 



AMERICAN EDITION REVISED AND BROUGHT TO DATE 

BY 

E. COLBERT, 

Formerly Superin'endent of Dearborn Observatory. 




CHICAGO AND NEW YORK? 

FAIRBANKS, PALMER & CO. 

1882, 



I OFYKIGHT BY 

Fairbanks, Palmer & Co. 

1 882. 



/ 



PREFACE. 

A great many people regard Astronomy as an in- 
tensely interesting- study ; yet allow their years to 
pass by without endeavoring to go beyond the phase 
of helpless wonder at the glories of the heavens. 
They would like to know something about the stars ; 
but do not try, simply because they consider the sub- 
ject to be beyond their reach, or at best, to be grasped 
only by dint of years of patient study under a master 
in the science. 

It is true, there is much more than enough material 
in the heavens for the study of any one lifetime. The 
phenomena of star motion present problems which tax 
the most powerful intellect, and some that undoubtedly 
lie above and beyond the ordinary comprehension. 
But the broadest facts are within easy mental reach ; 
and the fundamental principles of the science are not 
difficult to understand, as the result of a few hours 
patient reading. A few more hours will suffice to gain a 
" speaking acquaintance " with the more prominent 
stars — to recognize them when we see them in the 
sky, and to follow their changes of apparent position 
from hour to hour, and from month to month. This 
immense addition to the mental furniture may be 
(5) 



6 PREFACE. 

gained with no greater effort of the mind, and little 
more physical exertion, than is required to read an or- 
dinary novel. To proceed only so far will be to do 
well ; but most of those who have taken this first step 
are agreeably surprised to see how easily the rest 
opens out before them, and find genuine recreation in 
exploring what had previously seemed to be impene- 
trable mysteries. 

A careful perusal of this little book will enable any 
person of ordinary intelligence to understand the 
basic facts of modern astronomy ; and it will form a 
good foundation on which to build up a more compre- 
hensive knowledge of the science, if desired. 

Chicago, July 1st, 1882. E. 0. 



C0IS T TEIS T TS. 



CHAPTER I. 

ELEMENTARY IDEAS. 

Apparent Motions of the Stars, p. 9— Rotation of the Earth, 
11 — Its Form. 12 — Latitude and Longitude, Time, 15 — The 
Atmosphere, 20— Refraction and Twilight, 21. 

CHAPTER II. 

THE SUN. 

Apparent Motion of the Sun among the Stars, p. 23 — Equinoxes, 
25 — Right Ascension and Declination, 27 — Solar and Side- 
real Time, 28 — Equation of Time, 30 — Real Movement of the 
Earth, 31— The Seasons, 33— Sun Spots, 38— Rotation of the 
Sun, 39 — The Prominences and Corona, 40. 

CHAPTER III. 

THE MOON. 

Motion of the Moon. p. 44 — Her Phases, 47 — Eclipses, 50 — 
Harvest Moon, 54 — Distance and Size of the Moon, 55 — Her 
Path about the Earth and the Sun, 58 — Rotation, 59 — Ap- 
pearance of her Surface, Craters, Mountains, Plains, etc., 60 o 

CHAPTER IV. 

THE PLANETS. 

Apparent Motions with reference to the Sun of Inferior Planets, 
p. 62 — of Superior Planets, 66 — Apparent Motions with ref- 
erence to the Stars, 69 — Transits of Mercury and Venus, 72 — 
Th^ir use for finding the Distance of the Sun, 73 — Other 
Methods, 77— Kepler's Laws, 80— Gravitation, 82— Tides. 84 
— Masses of the Sun and Moon compared with that of the 

(7) 



3 CONTEXTS. 

Earth, 86— Mass of the Earth. 88— Bode's Law of Distances, 
89 — Appearance of the different Planets, 90 — Conditions to 
which they are severally exposed, 95. 

CHAPTEK V. 

COMETS. 

Apparent and Real Motions, p. 96— Their Aspects, 99— Their 
Physical Constitution. 100— Meteors. 101 — Remarkable Com- 
ets, 105 — Periodical Comets. 108 — Origin of Comets, 111. 

CHAPTEK VI. 

THE S-TARS. 

Their Number. Magnitudes, p. 115 — The Constellations, 118 — 
The Milky Way r 123 — Clusters and Nebulae, Ti-*'> — Laplace's 
Nebular Theory, 126 — Distances of some of the Stars. 128—- 
Proper Motions, 130 — Motion of the Solar System. 190 — 
Double Stars, 131 — Physical Constitution of Stars : 133— 
Temporary and Variable Stars, 134 — Precession and Nutation 
of the Equinoxes, 135 — Signs of the Zodiac, 136. 

Elements of Sun and Moon, 137. 

Elements of the Principal Planets. 138. 

Elements of Periodical Comets, 139. 



ELEMENTARY ASTRONOMY. 



CHAPTER I. 

The most casual observation suffices to show us 
that the sun rises in the east, gets gradually higher 
till it reaches its greatest elevation in the south,* 
when it begins to sink, finally setting in the west only 
to rise again in the east and perform the same round 
next day. 

If we turn to the stars at night we shall find some- 
thing similar, but on examining more closely it will be 
seen that some of them are longer above the horizon 
than others, and that certain stars never set but re- 
main constantly in view. If we watch these latter we 
shall find that there is one star which hardly changes 
its position, keeping constantly at nearly the same 
height, whilst the other stars appear to circulate round 
it at different distances. This star is called the pole- 
star, for a reason which will presently be apparent. 
Now amidst all this diversity of movement there is one 
feature which is common to all; it is that every star 
returns to the same position after the lapse of twenty- 
four hours, and in this interval it will have described a 
circle. This latter fact may be rudely verified as 
follows : — Joint two rods together like a pair of com- 
passes, and rest one of them in forks so placed that it 

*The reader is supposed to be in the United States, or other 
northern countries. For southern countries it will be sufficient 
to substitute south for north? 

(9) 



10 APPARENT MOTIONS OF THE STARS. 

points to the pole-star; then if the other rod be pointed 
to any other star it may be made to follow the star 
in its course by simply turning the first rod round in 
its forks, without altering the opening of the joint. 

The motion will be thus like that of a pair of com- 
passes, one leg of which is kept in an upright posi- 
tion as it turns. The second leg will, under these cir- 
cumstances, describe a circle, as may be seen by run- 
ning the upright leg through a sheet of cardboard (or 
stiff paper )held horizontally at such a height that the 
other leg, as it sweeps round, just touches it. 

If we look a little more closely we shall find that 
the fixed rod will not continue to point exactly to the 
pole-star all through its course, and that if we direct 
the rod in the forks to a point which is mid- way be- 
tween the highest and lowest and the most easterly 
and westerly positions of the pole-star, we shall get a 
point about which this star ( as well as all others ) de- 
scribes a circle, the other leg of our compasses follow- 
ing it exactly in its motion by simply turning about 
the fixed leg* This point is called the pole of the 
heavens, and the daily motion of the stars may be re- 
presented almost exactly by supposing them (as the 
Ancients did) to be fixed in a hollow globe which 
spins once in twenty-four hours round an axis passing 
through the pole, so that the stars would in that 
time describe circles of different sizes but all having 
their centres at the pole. But though this represents the 
movements of the stars, such a crystal sphere can 
have no real existence, for we shall presently see that 
the sun is more than ninety millions of miles off, and 
the nearest of the stars are hundreds of thousands of 
times that tremendous distance from us, and a material 

* A telescope mounted on one of the leers of our compasses so 
as to follow any star in its daily motion by simply turning about 
the other leg ( which is then called the polar axis ) is termed 
an equatorial. The turning of the axis maybe effected by 
means of clock-work, and the telescope will then continue to 
point to the star for a leng:h of time, during which it can be 
steadily gazed at. 



BOTATION OF THE EARTH. 11 

sphere of that size spinning round once a day is of 
course quite out of the question. We are thus led to 
conclude that the diurnal motions of the stars cannot 
be real, but are only apparent, arising from our own 
movement in an opposite direction, just as when we 
spin rapidly round in one direction, the chairs, tables, 
and other objects in the room all appear to turn round 
at the same rate but the opposite way, the part of the 
ceiling directly overhead being the only point which 
appears stationary, just like the pole of the heavens. 
And this gives us some clue as to what our real move- 
ment and that of the earth, on which we stand, must 
be. The earth must be spinning round an imaginary 
axis, pointing nearly in the direction of the pole-star, 
and carrying us and all terrestrial objects round with 
it once in twenty-four hours. But if we accept this 
explanation, how will the shape of the earth accord 
with such amotion ? The portion of the earth which 
we can see at any one time appears a flat (or undulat- 
ing) plain, bounded by a line — the horizon — where 
the sky seems to meet it; but we must not hastily 
conclude from this that the whole earth is a flat 
plain, for what we see is only a perspective view of a 
very small portion. If we look out over an expanse of 
sea (which is free from the irregularities of the land) 
it will be easy to assure ourselves that it is not really a 
plane,* for ships appear to sink lower and lower as 
they move away from us, so that first the hull and then 
the lower sails are cut off by the sea between us and 
the ship, whilst on ascending a cliff the lower sails 
and hull again come into sight. This shows that the 
surface of the sea is really curved (convex), for we 
know that objects disappear behind an undulation 
of the ground in exactly the same way, and that 
by ascending a hill they come into view again as 

* A plane is a flat surface, like an extremely thin sheet of 

Saper, or the surface of a table, but of unlimited extent. Thus 
le plane of a circle is the flat surface in which the circle lies, 
boundless in every direction. 



12 FORM OF THE EARTH. 

soon as the visual line from the object to our eye 
clears the top of the swell in the ground. 

There is another circumstance which now helps us 
materially in Ending the shape of the earth. Wherever 
we are, whether on the top of a mountain or on board 
a ship at sea, the portion of the earth which we can 
see, always appears a circle ; though when we are at 
a considerable height, this circle seems much smaller, 
whilst we really see a larger portion of the earth's 
surface. Now the only figure with which we are ac- 
quainted that appears circular from all points of view 
and at all distances, is a globe; and further, we know- 
that this seems to grow smaller as we remove the eye 
from near its surface, whilst the actual portion of it 
which we see is really larger. This may readily be 
verified by means of a terrestrial globe or a large ball, 
but it must be remembered that in the actual case the 
distance from the earth's surface to which we can get 
would be represented on an 18-inch globe by about 
the thickness of a sheet of paper. From all this we 
infer that the earth is a globe, which rotates about an 
axis nearly in the direction of the pole-star, and this 
conclusion is supported by what is observed of the 
motions of the stars in other countries. Any one who 
makes a voyage to southern latitudes will observe that 
the pole about which the stars revolve, while keeping 
the same position near the pole-star, appears to sink 
as he journeys south, in consequence of which those 
stars, which "are only just visible in these climes in the 
southern horizon, get higher and higher, and new con- 
stellations come into sight. This goes on till the pole- 
star sinks in the northern horizon, when it is seen 
that there are really two poles about which the heavens 
appear to turn, one on the northern and one on tl e 
southern horizon; from which it is clear that the direc- 
tion of the axis of motion is in the horizontal plane. 
The point of the earth at which this is the case is said 
to be in the equator, because it is equidistant from the 
two poles of the earth. The celestial equator is a 



ITS POLES. 13 

great circle,* of which the plane is parallel to the 
earth's equator, and which, therefore, lies half-way 
between the poles of the heavens. It is advisable 
here to distinguish clearly between the pole of the 
heavens and the pole of the earth. The former is 
simply the direction of the line about which the stars 
appear to turn, or about which the earth really turns, 
whilst the latter is the extremity of the axis through 
the earth's centre about which it turns, and it has, 
therefore, a definite position on the earth as well as a 
definite direction in space. As there are two ends to 
a straight line, there are of course two poles, which 
are distinguished as north and south. To return to 
our traveller. After crossing the equator he will find 
that the southern pole (though it is not distinguished 
by any bright star near it like the pole-star) rises 
higher and higher till it reaches the same height 
above the southern horizon as the north pole had 
originally above the northern, when the traveller has 
traversed the same distance south of the equator as 
he had previously done before reaching it ; and he 
will fnrther have remarked that the north pole sinks, 
or the south pole rises, through an angle of one de- 
greef for every sixty-nine miles he travels south. 

All this is exactly what we should expect if the 
earth be a globe spinning about an axis, for in this case 
this axis, being in the direction of the pole of the 
heavens, would remain fixed among the stars, whilst 
the horizon (which is the direction of the surface 
where the spectator is) would change as the observer 
moved, so that instead of the pole-star approaching 
the horizon, it is really the horizon which approaches the 

* A great circle of a sphere (or globe) is one of which the 
plane passes through the centre of the sphere, dividing it into 
two equal parts or hemispheres. A small circle divides the 
sphere into two unequal parts. 

t A right angle, which is the angle of a square or that 
formed by two perpendicular lines, is divided into ninety equal 
parts, called degrees, ninety degrees being usually written thus 
90°. 



14 SIZE OF THE EARTH. 

direction of the pole-star. At the equator the pole-star 
will be in the horizon, and will rise one degree for every 
69 miles we travel north (owing to the tilting of the hori- 
zon), until at the pole, after having travelled over 6,200 
miles, it would be 90° high, or in the zenith.* Hence 
the circumference of the earth, which is four times the 
distance from the equator to either pole, is 25,000 
miles about, and the diameter 7,900 miles, the .circum- 
ference of a circle being about 3 1-7 times its diameter 
(more exactly 3*1416). Strictly speaking the earth is 
not a perfect globe, but more like an orange, bulging 
out slightly at the equator, a result of its spinning 
round so rapidly, which tends to throw the particles at 
the equator off, like mud from a rapidly moving car- 
riage wheel. The amount of this bulging is however 
very small, being only 13^ miles. As a point on the 
earth's equator moves round in a circle of the above 
size in one day, it must be moving at the rate of over 
1,000 miles an hour, or 1,500 feet a second, which is 
more than the speed of a cannon ball. This motion 
is so smooth, however, that we feel nothing of it, as all 
the objects round us on the earth (including the at- 
mosphere) move together with ourselves. But if it 
were not for the attraction of the vast mass of the 
earth, which pulls all bodies towards its centre (making 
a stone thrown up in the air fall back to the surface), 
we should fly off just as a stone whirled round in a 
sling does when the pull of the string is let go. It 
may seem very difficult to believe that we can really be 
moving at such an enormous speed, but unless we 
admit this motion we must suppose the stars to be 
swung around us with a velocity many million times 
greater; and, besides this, there is direct proof that 
the earth is moving in the way we have explained. 
This is given by the gyroscope, which is nothing but a 
top with a heavy disc, suspended in gimbals, so that 
it is free to turn in any direction. When this is set 
spinning rapidly, it requires great force to twist it out 

* The point directly overhead. 



LATITUDE— TIME. 15 

of its direction, as any one may readily experience 
with the ordinary toy gyroscopes. If left to itself, then, 
we know that its axis will continue to point in the same 
direction, and as it appears to follow a star, to which 
it is once pointed, in its daily course from rising to 
setting, we may conclude that the star is really fixed, 
and the motion which it appears to have in common 
with the gyroscope is really caused by the spinning of 
the earth about its axis once in every twenty-four 
hours. 

From what precedes, we see that the elevation of the 
pole measures the distance of the observer from the 
equator; and this is called the latitude of the place, 
north or south, as the north or south pole of the heav- 
ens is elevated. This latitude is measured in degrees, 
the distance from either pole to the equator being 
ninety degrees, or in other words, the latitude of the 
pole is 90°. The equator being the line formed by 
all points which are equidistant from the two poles, 
will be a circle, and, further, all places which have the 
same latitude, being at the same distance from the pole, 
will lie on a circle parallel to the equator; this is called 
a circle of latitude. Thus when we say that a place 
has a certain latitude, we fix its position so far as to 
settle that it lies somewhere on a certain circle, which 
is determined by measuring the elevation of the pole. 
This is readily done; for the pole lies midway be- 
tween the highest and lowest positions of the pole-star, 
being at the centre of the circle w T hich this star de- 
scribes, and it is only necessary to measure the an- 
gular elevations above the horizon of this star at its 
highest and lowest points by means of a divided circle. 
The same method would answer equally well if applied 
to any other star tolerably near the pole. But to fix 
the position of any place on the globe it is necessary to 
know whereabouts on the circle of latitude it lies, and 
this is practically a more difficult matter, and one that 
requires for its determination, astronomically, the in- 
troduction of a new element — time. For the mea- 
surement of time uniform motion is required, and 



16 TIME— THE MERIDIAN. 

this condition is secured more or less perfectly in the 
motion of the hands of a clock under the control of a 
pendulum, or of a watch or chronometer regulated by 
the balance and its spring ; but the rotation of the 
earth supplies us with the only perfect timekeeper with 
which we are acquainted, and the apparent movement 
of the stars resulting from it, really serves to regulate 
all our clocks and watches. In fact the heavens may, 
for this purpose, be compared to one of those lamp 
clocks in which the globe turns round and brings the 
hours painted on it up to an index. The stars re- 
present the hours and minutes, though not placed at 
regular intervals : but where are we to find the index 
which is to tell us the time? We must look for this 
in the movements of the stars themselves. We saw 
that they describe circles about the pole, so that 
their paths are tilted with reference to the horizon ; the 
highest point of the star's course will evidently be a 
convenient point to which to fix our index, and a little 
consideration will show that the highest point of each 
circle will be where it meets a vertical plane through 
the north and south points (or in other words, through, 
the zenith and pole): for the leg of the compasses, of 
which we have spoken before, and which we suppose 
to follow the course of any star, will evidently reach 
its highest point when the plane formed by the two legs 
(one of wdiich points to the pole) is vertical. This plane 
then, which is called the meridian, may be taken as our 
index. Though this is only an imaginary index, it can 
be used as readily as if it really existed in the heavens, 
by simply mounting a telescope on trunnions, hke a 
gun, and making it swing vertically, north and south, 
so as, at the proper elevation, to point exactly to the 
pole.* When such a telescope points exactly to any 

* A Telescope so mounted is called a transit instrument. For 
greater accuracy it is provided with cross wires lor spider 
threads) fixed at the place where the image is formed, bo ii- t" 
mark the centre of the field. These cross wires being Been .it 
the same time as the star, enable us to judge when the telescope 
is pointed exactly to it. 



LONGITUDE. 17 

star, we know that the star has come up to the Index, 
and when it next comes up to this position we know 
that exactly twenty four hours have elapsed, and if our 
clock does not indicate the same time as before, we 
know at once that it has gained or lost so much in the 
day. It is thus easy to find how our clock is going ; 
but to tell the time at any instant it is necessary to 
know the intervals at which the stars are placed on our 
celestial clock, and this can best be done by noting 
with our clock the difference of times between the 
arrival of pairs of stars at the index (their meridian 
passage or transit as it is called) and correcting this 
for the proportional gain or loss of the clock in the 
interval, on the assumption that it has gone uniformly 
for twenty-four hours; by repeating such observations 
a great many times and taking the average, the irreg- 
ularities of the clock will, on the whole, nearly balance, 
and an accurate measure of the interval of transit of 
each pair of stars be arrived at. Thus taking any par- 
ticular star as our starting point for h , Ave can easily 
find the time at any other part of the twenty- four hours. 
But it is more convenient for purposes of ordinary 
life to take the sun as our starting point, though on 
account of his irregular apparent motion among the 
stars (which will be discussed more fully in the next 
chapter), he does not make quite such a good clock as 
the stars, gaining at certain parts of the year and 
losing at others, so that we must make allowance for his 
being so many minutes fast or slow, just as with an 
ordinary clock. The time at which the sun comes up 
to our index is called apparent noon, and if we make 
allowance for his being fast or slow, we readily get the 
instant of mean noon (as it is called) at which our 
clocks ought to point exactly to h . 

We may now proceed with the question of longitude. 
For convenience of illustration we compared the heavens 
to a globe which turned round and brought the hours 
up to a fixed index, but really it is the celestial globe 
which is fixed and the index or meridian which moves. 
Now let us take two places with two different indexes, 



18 WASHINGTON TIME. 

or meridians, which, by the rotation of the earth, arc 
brought up successively to the sun, giving the instants 
of noon for the two places respectively. When it is 
noon for the second place the sun will be west of the 
meridian at the first, and the time that has elapsed 
since the sun was in the meridian of the first place, 
will be the same part of the time between successive 
returns of the sun to this meridian, as the angle turned 
through by the earth to bring the second meridian up 
to the sun (from the position for noon at the firsl 
station), is of the angle turned through from one noon 
to the next. The same would hold for the stars, moon, 
or planets, and the difference of longitude of the two 
places will be the same partof 24* if expressed in time, 
or of 360° if expressed ■ in angular measure. The 
longitude of a place, then, is nothing but the difference 
between its time and that of the place selected as our 
starting point (Washington for the United States), so 
that having the means of determining local time (e. <jr., 
noon) at any place (as explained above) what is wanted 
is a means of knowing Washington time. We may men- 
tion here two ways of obtaining this knowledge, reserv- 
ing that which depends on the motion of the moon, 
and which is so extensively used at sea, for a future 
chapter. The first method to which we shall refer 
makes use of chronometers. Thanks to the improve- 
ments effected in its construction, under the stimulus 
of large rewards offered by the government of Eng- 
land, this refined form of watch may be relied on to 
give Washington time within two or three seconds 
(corresponding to about half a mile in the deduced 
longitude) after a voyage of a week or ten da; 
that the longitude may be found to that degree of ac- 
curacy after a short voyage. But there is another 
method of far greater accuracy which has been intro- 
duced of late years in England wherever the telegraph 
extends to. In this method standard time is obtained 
by a signal sent from the Royal Observatory at a 
known instant of Greenwich time ; such signals are 
sent out every morning at 10 h a. m., at noon, and at 1 



CIRCLES OF LATITUDE AND LONGITUDE. 19 



p.m. exactly, and are distributed all over the United 
Kingdom by the post-office telegraphs, their chief 
use being to regulate time on railways and in public 
buildings. 

From what precedes it is clear that the position of 
any place on the earth is completely determined when 
we know the circle of latitude on which it lies, and al- 
so its position on that circle, i. e., its latitude and 
longitude ; but the reader has, perhaps, not got a very 
clear idea of what is represented by longitude on the 
earth itself. To assist him in this, we should explain 
what is meant by a meridian on the earth, having al- 
ready explained what is the astronomical meridian of 
a place. If we start from any place and travel due 
north or due south we shall always remain in the same 
vertical plane through the pole, which will therefore 
continue to be our meridian, so that all the places 
we pass through will have their noon at the same 

instant, and therefore 
have the same longi- 
tude. The line along 
which we travel is 
called a terrestrial me- 
ridian, and, since we 
are evidently going di- 
rectly towards the pole, 
all meridians will pass 
through the poles. We 
may, therefore, con- 
ceive the earth as di- 
vided into a series of 
circles of latitude, all 
parallel to the equator, 
and into a series of circles of longitude, or meridians, 
all passing through the poles, which, by their cross- 
ing, define the positions of places on the earth. These 
are the lines which are drawn on maps, though for the 
sake of clearness only those at convenient intervals are 
put in; it is, however, necessary to imagine a circle of 
latitude and one of longitude passing at right angles 
to each other through every point of the map. The 




20 THE A TMOSPHERE. 

figure represents the circles of latitude drawn for 
every 10°, and the meridians for every hour; the num- 
bers placed between the meridians of I h and IP rep- 
resent the number of miles traversed by places on the 
corresponding circles of latitude in one hour. 

We have not yet spoken of a very important part of 
the earth, and that which, in fact, renders our globe 
habitable — its atmosphere. At every point of the sur- 
face we find air, which makes its presence felt in 
various ways, and which exerts a pressure of 15 lbs. on 
every square inch of surface of a vessel from which 
the air has been exhausted. This pressure can be 
measured accurately by the mercurial barometer, an 
instrument in which the pressure of the air on the 
mouth of a vertical tube, closed at the upper end and 
exhausted of air, is balanced by the weight of mercury 
which it will hold suspended. It is in this way found 
that the pressure at the sea level is nearly the same at 
all parts of the earth, being equal to the weight of a 
column of mercury about 30 inches high, and having 
the same section as the surface on which the pressure 
is exerted, which corresponds to a column of air of the 
same density throughout as that at the surface, and 
27,000 feet, or about five miles high. But on rising 
above the sea level, whether in ascending a mountain 
or in a balloon, we soon find that the pressure decreases 
less rapidly than would be the case if the atmosphere 
remained of the same density as at the surface : thus 
we have to ascend to 2,850 feet to get through the first 
tenth of the atmosphere ; through 3,200 feet more to 
get through the next tenth ; through 3,650 feet more 
for the third tenth; and 4,250 feet more for the fourth 
tenth, and so on. In this way it would require an 
ascent of about 18,000 feet to pass through the lower 
half of the atmosphere (as measured by its weight) 
and an ascent of about 30,000 feet to traverse the lower 
two-thirds, starting in each case from the sea level. 
Since the pressure of the atmosphere is due to the 
weight of the superincumbent air, it is easy to see 
that the air gets lighter, and therefore less dense, 
as we ascend, and this is in perfect accordance with 



REFRACTION. 



21 



the law that elastic gases expand, and so become rare- 
fied, as the pressure is diminished. Thus we see that 
the earth is surrounded by a shell of air in contact 
with it, and decreasing in density as we proceed out- 
wards, so that at a height of less than ten miles it is 
too rare to be capable of supporting human life. Small 
though the extent of our atmosphere is, as compared 
with the size of the earth, it modifies in a wonderful 
degree the climate of our globe, and further gives rise 
to two important astronomical phenomena — refraction 
and twilight. When a ray of light passes from one 
medium into another which is more dense, it is bent 
away from the surface of the dense medium. This is 
precisely what happens when a ray from a heavenly 
body enters our atmosphere from outer space ; and as 




REFRACTION. 



The rays from two stars corning to the observer at o, along 
s^o, s s p 8 o, are bent downwards in passing through the 
atmosphere, and reach the observer in the directions of the 
dotted* lines QaO,Q 2 o, along which the two stars are seen. 



the layers get more and more dense, it gets more and 
more bent away from the surfaces of the layers (which 
are parallel to the horizon ) in its passage through the 
atmosphere to the earth's surface. Thus the rays 
from a star which enter the atmosphere in a certain 
direction sp will, when they reach us, have a direc- 
tion qo further away from the horizon, and as the star 
is seen in the direction which the rays from it have 
when they fall on our eyes, it will appear higher than 



TWILIGHT. 



its true position, owing to the effect of the atmosphere. 
This effect is called refraction, and its amount is greater 
the nearer the bodv is to the horizon. The consequence 
of this is that the northern stars do not appear to 
describe exact circles about the pole, the lower half ol 
their course being very slightly flattened, as they are 
raised more by refraction in the part near the horizon 
than when they are higher in the upper half of their 
paths. This effect is, however, in most cases very 
slight, not being perceptible to the naked eye, and 
when allowance is made for it the diurnal arcs are 
found to be true circles. Another effect of refraction 
is that the day is lengthened at the expense of the 
nicrht ; for when the sun is really on the horizon, he is 
apparently raised above it by more than his own 
diameter, and has, therefore, this space further to travel 
before he sets, causing a delay of about 2 m . Similarly 
his rising is hastened, so that the day is lengthened by 
some 4 m . But twilight has afar more important effect 
for practical purposes on the duration of daylight; for 
after the sun has set he still continues to illumine 
the clouds and upper regions of the atmosphere, and 
this light is reflected irregularly in all directions, some 
of it reaching that part of the earth which would other- 
wise be in absolute darkness after the sun had set. It 
is found by observation that twilight ceases to be per- 
ceptible when the sun is more than 18° below the 
horizon, and it results from this, that at a height of 50 
miles, or about an eightieth part of the earth's radius, 
the atmosphere is too rare to sustain particles capable 
of scattering the sun's light. As the duration ot twi- 
light is simply the time taken by the sun to descend 
18° below the horizon, it follows that twilight is much 
shorter in tropical countries, where the sun descends 
perpendicularly to the horizon, than in polar regions, 
where his course is oblique, the pole being considerably 
elevated and the equator much inclined to the horizon. 
The diffused light of day may be referred to the same 
cause as twilight— the scattering of the sun's light by 
particles of vapor in the air, more especially in the 
form of clouds. 



APPARENT MOTION OF THE SUN. 23 



JHAPTER II. 

In the last chapter the apparent diurnal movement of 
the heavens (in which all the heavenly bodies partake) 
about the pole was dealt with. It is now time to treat 
of the apparent motions of some of these bodies among 
the stars, which, though much smaller in amount than 
the diurnal movement, yet affect it appreciably in 
certain cases. We will begin with the sun, as its move- 
ments are the most important, and at the same time the 
simplest. We have seen that all the heavenly bodies 
have a diurnal motion about the pole in the direction in 
which a right-handed screw would be turned to screw it 
in at the north pole, or in the direction of the hands of 
a watch, which faces the north pole ; and the sun, moon, 
and planets have the same general motion, though very 
slightly altered in amount by their apparent motions 
among the stars. If an observer notes at midnight the 
position of any bright star (south of the zenith), he will 
find at midnight a fortnight after, that it has got con- 
siderably to the west of its former position, and that it 
really was in that place an hour earlier, or at eleven 
o'clock. It is therefore evident that the stars have 
gained an hour on the clock, or, what comes to the 
same thing, that the clock has lost an hour on the stars. 
But the clock is regulated by the sun, so that the sun 
has been lagging behind the stars, or moving eastward 
among them at the rate of 4 m a day, or of an hour 
nearly in a fortnight. Our observer would find, on 
continuing his observations, that another hour was lost 
by the clock or gained by the star in the next fortnight, 
and so on, till the star finally disappeared in the even- 
ing twilight. He could then take another star, and in 
this way would find, as the general result of his observa- 
tions, that his clock continued to lose uniformly at the 
rate of 4™ a day, and that at the end of one year it 
had lost 24 hours, having made the complete tour of 
the stars, so that the original star was again in its 
original position at midnight. The sun would thus 



24 APPARENT PATH OF THE SUX. 

have gone completely round among the stars in dne 
year, but it would have differed from the clock in this, 
that its lagging behind the stars would not have been 
uniform from day to day, being, at certain seasons 
of the year, rather more than 4 m a day, and at others 
rather less. For though our ordinary clocks are regu- 
lated primarily by the sun, they do not indicate Ap- 
parent Solar Time, as shown by a sun-dial, but what 
is called Mean Solar Time, which is obtained by 
making a correction for the irregularity of the suivs 
motion. It is this irregularity that we wish now to 
determine, and for this purpose we must refer to the 
stars, which are, as already explained, our only reliable 
time-measurers. 

But before considering more fully the sun's motion, 
we must find out more precisely the exact path among 
the stars which he describes. Every one has remarked 
that the sun attains a greater height and is longer 
above the horizon in summer than in winter; and 
from what has been said in the first chapter it will 
readily be understood that for this to be the case the 
diurnal arc which he describes must be nearer the 
north pole in summer than it is in winter; in fact he 
is in summer north of the equator, and in winter 
south of it; but to learn more of his path recourse 
must be had to actual measurement of his distance 
from the equator at different times of the year. 
This can best be done by measuring at noon his an- 
gular distance from the zenith, and taking the differ- 
ence between this and the distance of the equator 
from the zenith, which is equal to the latitude of the 
place (the celestial equator being vertical for any place 
on the earth's equator, and tilting one degree towards 
the south, as the north pole rises, for every degree of 
north latitude). Now the zenith distance of any 
heavenly body when on the meridian may be readily 
measured by attaching a vertical graduated circle oi 
arc of a circle, to the transit instrument described in 
the last chapter, so as to turn with the telescope. Such 
a circle will, if we have a mark on it to which an 



EQUINOXES. 25 

index points when the telescope is directed to the 
zenith, show by the position of the index on the circle 
the angle through which the telescope has turned 
from the zenith when it points on any object, such 
as the sun : in other words, it will show the meridian 
zenith distance of the sun. But we must first fix our 
mark, and this is best done, not by pointing the 
telescope vertically up, but indirectly. We know that 
the reflection of a very distant object in a lake ap- 
pears depressed just as much below the horizon as the 
object is elevated above it, whatever be our height 
above the surface, a result which follows from the fact 
that the surface of water or any other fluid is horizon- 
tal. If, then, we point our telescope to the reflection 
of a star in a basin of water, or, still better, in a basin 
of mercury, we shall have to depress the telescope 
through an angle equal to that through which we 
have to raise it to point at the star directly, and if 
the position "of the index on our graduated* circle 
be noted in each case, the point half-way between 
the two will evidently correspond to the horizontal 
position. The mark for the zenith will have to be 
made at a point 90° from this, the zenith being 90° 
distant from aiy point of the horizon. Measures of 
the sun's me idian zenith-distance being made in 
this way, and his distance north or south of the 
equator deduced from our knowledge of the latitude 
of the place, that is, the elevation of the pole, it is 
found that there are two days of the year exactly 
six months apart, viz., March 20 and September 22, 
when he crosses the equator. These points of cross- 
ing are called the equinoxes, because the day and 
night are then exactly equal all over the world, the part 
of the equator above the horizon being in all latitudes 
equal to the part below, so that a star or other heavenly 
body which is in the equatoris 12 hours above the 
horizon and 12 hours below wherever the observer may 
be situated. At the vernal equinox, corresponding to 
March 20, the sun passes from south to north of the 
equatjr, and gets further and further north, but at a 



26 THE YEAR— LEAP YEAR. 

slackening rate, till June 21, the summer solstice, when 
he is about 23^° north of the equator; this is his turn- 
ing point, ancf he then begins to approach the equator 
again, his distance from it decreasing at first very 
slowly, and then more rapidly, till he again crosses 
it at the autumnal equinox, but this time from north to 
south. His southward motion continues til! December 
21. the winter solstice, when he begins to move north- 
ward, arriving at the vernal equinox again on March 20. 
The time that elapses between the returns to the 
vernal equinox is not an exact number of days, being 
365 d 5 h 48 m 50 s in solar time, or 366 d 5 h 48 m 50* in 
sidereal time, there being one more sidereal day from 
the circumstance that the sun has gone round once 
eastward in the direction in which the earth spins, 
lagging continually behind the stars in its rising and 
setting. In order that the seasons may always fall at 
the same times of the civil year it is necessary to take 
account of the fraction of a day (nearly a quarter) 
over the 365 ; in the Gregorian calendar, which is that 
adopted generally; this is effected by making every 
fourth year (leap year) consist of 366 days, the extra 
dav being added to February ; but as the true year is 
really rather less than 365^ days, the extra day is not 
added to any year which is an exact hundred, and 
would, therefore, naturally be a leap year ( e. </., 
1700, 1800), unless the number of the century is also 
divisible by 4 (e.g., 1600, 2000), and in this way 
three days are got rid of in every 400 years, making 
the discordance between the civil year and the truth 
less than one day in 3,000 years. 

It will be readily' understood that as the sun takes 
six months to move from 23^° south to 23£° north, the 
change of declination or distance from the equator in 
one day is very small, in fact it is never more than 
four-tenths of a "degree .(less than the sun's diameter), 
so that the diurnal course remains very nearly a circle 
described about the pole just as in the case of a star. 

Before proceeding further it is desirable to explain 
how the position of a heavenly body is fixed. For a 



RIGHT ASCENSION AND DECLINATION. 27 

place on the earth we saw that its latitude, or the ang- 
ular distance of the point from the equator, and its long- 
itude, i. e., the time required for the earth's rotation to 
bring the meridian of the place to the position orig- 
inally occupied by the first meridian, or that through 
Washington, are sufficient to fix the position of the 
place. Now the same system may be adopted for the 
stars, but in their case the angular distance from the 
celestial equator is called Declination; and correspond- 
ing to longitude reckoned from an arbitrary first 
meridian we have Right Ascension, measured from 
the vernal equinox, in exactly the same way, i. e., by 
the time which elapses before the meridian through 
the star occupies the original position of the meridian 
through the vernal equinox. We have here used the 
term meridian in the same sense in which it is used 
for the earth, but to avoid confusion with the fixed 
meridian, the great circle drawn from the pole through 
any star is called the hour circle of that star. Thus 
we have imaginary circles of declination and hour 
circles through every point of the sphere on which the 
stars appear to be projected, just as we have through 
every point of the earth circles of latitude and merid- 
ians.* Declination and Right Ascension, then, are 
to be considered as corresponding on the celestial 
globe to Latitude and Longitude on the earth ; 
unfortunately the terms Latitude and Longitude in the 
case of the heavenly bodies have been applied to a 
totally different system of measurement, a circum- 
stance that has given rise to some confusion of ideas. 
So far we have spoken of time as determined 
from the sun and from stars, without pointing out the 
distinction between the clocks, which are used in the 
two cases. A solar clock is regulated to show h at noon 
and 11 again at the next noon, but if such a clock were 
used for stars it would be found to have lost nearly 4 m 

* The circles on the Key Map ( Frontispiece ) represent the 
circles of 60° and 30° North Declination, the Equator and that 
of 30° South. The lines from the center represent the Hour 
Circles for every two hours. 



28 SOLAR AND SIDEREAL TIME. 

between the successive passages of the same star across 
the meridian, in consequence of which we use for the 
stars a sidereal clock, which is so regulated that exactly 
24 of its hours elapse between successive transits of the 
same star. Such a clock is set so as to indicate h ex- 
actly when the vernal equinox is on the meridian, and 
as this point may be taken as fixed among the stars, 
and therefore takes 24 sidereal hours to return to the 
meridian, it is clear that sidereal time must be used for 
right ascension, which measures the distance from the 
vernal equinox. With regard to terrestrial longitudes, 
we must use a solar or sidereal clock, according as we 
take transits of the sun or of a star across the meridians 
of the two places. What we really want in this case is 
the proportion that the interval of time between the 
transits of the same heavenly body over the two me- 
ridians bears to the interval between its successive 
transits over the same meridian, and this proportion is 
the same whether both intervals are expressed in solar 
or in sidereal hours, but it is convenient to take the 
second interval as 24 h (solar or sidereal, according as 
the sun or a star is used), and this determines whether 
the first is to be in solar or sidereal hours. The same 
consideration applies to all cases where time is used to 
measure the angular distance of two points. A homely 
illustration may put this in a clear light. In some 
parts of England a pound of butter is made into a roll 
a yard long, and sold by length. Suppose, now, that 
in France a pound of butter is made into a roll a metre 
long, then we shall clearly get the same quantity of 
butter whether we buy a quarter of a yard in England 
or a quarter of a metre in France ; but if we buy a 
quarter of a yard in France we get less, and if a quarter 
of a metre in England more than our quarter of a 
pound. We have dwelt on this point because it is 
usually troublesome to beginners, from the want of a 
clear conception of the measure that is being used. 

To return to the sun. We have shown how to meas- 
ure his declination. To find his right ascension we 
must first find the right ascensions of one or more stars 



ECLIPTIC. 29 

by rioting the difference of the times of transit (in 
sidereal hours) of the sun when he crosses the equator 
at the vernal equinox, and of the selected stars, and 
then observe the interval (also in sidereal time) between 
the transit of one (or more) of the known stars and of 
the sun. The sun's right ascension will be found by 
adding this interval to the star's right ascension. If 
several stars be observed, the mean (or average) of the 
results from each star can be taken, and the final result 
will then be more accurate. This is a principle which 
is continually made use of in astronomy (and other 
observational sciences) to reduce the inevitable errors 
arising from the imperfections of our senses and of 
our instruments, all which affect a single observation, 
but very nearl}- balance one another when we take the 
mean of a large number of measures of the same 
quantity; the errors which make it seem too big, being 
about as many as those wdrich make it too small, on 
the principle that if a coin be tossed up a large number 
of times, it will turn up heads about as many times as 
it does tails. The sun's position being thus found for 
every day of the year, we can plot down his course on 
an artifical globe, and we find in this way (or by calcu- 
lation) that his apparent path is a great circle * inclined 
to the equator at an angle of 23^-, and cutting it at the 
equinoxes. The plane of this circle is called the ecliptic. 
The sun's motion along this path is not quite uniform ; 
about January 1 it is quickest, and about July 1 slowest, 
but the variation is only about X V of the whole, the 
daily motion ranging from 57' to 61'. This variation, 
combined with the tilt of the sun's path, which makes 
his motion more oblique to the equator at the equinoxes 
than at other times, causes an irregularity in the time 



*Any body which moves in a plane passing through the spec- 
tator, no matter what the path in that plane he, will appear to 
describe a great circle in the heavens, since a great circle is the 
curve in which the sphere is cut by a plane through the ceuter, 
?'.e.,' the spectator, and we refer the actual path to the sphere of 
the heavens, by looking along the plane in which it lies. 



30 EQUATION OF TIME. 

as shown bv the sun, and if a clock be regulated to go 
uniformly with the sun's average rate, the sun will be 
at certain times of the year fast or slow by the clock 
to the extent of 16 minutes, the amount by which the 
sun is fast or slow being called the equation of time. 

Further, the change in the sun's rate of motion is 
accompanied by a corresponding change in his ap- 
parent diameter, which is largest when the motion is 
quickest, the variation amounting to about a thirtieth 
part of the whole.f When an object increases in 
apparent size, either it must really be growing larger, 
or it must be approaching us. Now, in the case of the 
sun, we have no reason to conclude that there is any 
real change of diameter, such an alteration of bulk 
beincr highly improbable, and we are therefore led to 
inferthat he is nearer to us in January than in June 
by about ong-thirtieth part. t 

If now we draw a circle to represent the ecliptic, 
and lay down on it the position of the sun on every 
fifth day of the year, the lines drawn from the center 
to these points will represent the directions in which 



* The sun and clock are together four times in the year, via. .:— 
On April 15, June 14, Sept. 1 and Dec. 24 ; from April 15 to 
Jane 14, and from Sept. 1 to Dec. 24 the sun is last, the great- 
est error in the first period being nearly 4 m on May 14 and in 
the second period 16K m about Nov. 3. From June 14 to Sept. 
1, and from Dec. 24 to April 15 the sun is slow the greatest 
error in the first period being 6M m on July 26 and in the second 
neriod 14^ m on Feb. 11. As the sun is steadily losing on thy 
clock from Nov. 3 to Feb. 11, his rising and setting will both 
be retarded from this cause, and thus the eveninga will lengthen 
more than the mornings at the beginning of the year, though 
this effect is only apparent, being the result of our reckoning 
by clock time instead of sun time. 

+ There is a curious optical illusion which makes the sun and 
moon seem much larger when close to the horizon ; but this is 
only the result of having known objects, as trees and houses, 
to compare them with, which enables us to realize to acertam 
extent how immensely distant these heavenly bodies really axe. 
The angular diameters (when carefully measured and cor- 
rected for refraction, which slightly decreases the diameter ) 
agree exactly with the results of observations near the zenith. 



OB BIT OF THE EABTH. 31 

the sun is seen by us at the corresponding times ; 
but as his distance changes, we must, to represent his 
apparent motion fully, set off on these radii lengths 
corresponding to his actual distance on these days. 
We thus conclude that the sun appears to move round 
us once a year in a slightly oval and eccentric path. 
But we have, so far, no more reason to suppose that 
the sun is moving; round the earth, than that the earth 
is moving round the sun, for either supposition would 
.explain the sun's apparent motion, just as we saw that 
the apparent rotation of the heavens may be explained 
by a rotation of the earth in the opposite direction. 
Now there are several circumstances which lead us to 
conclu le that it is the earth which goes round the sun 
and not the sun round the earth. In the first place, 
the sun is enormously bigger than the earth, as we 
shall see when we come to discuss the means of find- 
ing his distance, which are quite independent of this 
question. Then, again, we shall find that there are 
other heavenly bodies of which the apparent move- 
ments can only satisfactorily be explained by suppos- 
ing them to revolve about the Sun, at distances which, 
in the case of some of them, are many times that of 
the earth from the sun, and as these bodies themselves 
are generally larger than the earth, the supposition 
that the sun is carrying such masses along with him 
in his course round our diminutive earth is in the 
highest degree improbable. But it is when we come 
to discuss the physical cause of these motions that the 
absurdity of such an hypothesis is brought home to us. 
In anticipation, then, of the conclusions of sub- 
sequent chapters, it may be stated that the earth 
revolves round the sun once in a year in a slightly 
oval and eccentric path in the plane of the ecliptic, 
at a distance of about 23,400 of the earth's semi- 
diameters, and with an average velocity of 18 miles a 
second ( more than fifty times as fast as a cannon ball), 
moving over eight times her own diameter every hour. 
As the sun's apparent diameter is 32', or rather more 
than half a degree, at his mean distance, it follows that 



32 RELATIVE MOTION— THE SEASONS. 

he is at a distance from us of 215 times his own semi- 
diameter, which is 109 times that of the earth.* 
Now although we may at first feel some difficulty in 
realizing that our globe is moving at such an enormous 
speed without our being conscious of it, yet if we con- 
sider that the earth bears the same proportion to the 
sun that a small pea bears to a 12-inch globe, we shall 
find it far more difficult to conceive that sue!) an in- 
significant body as our earth is really the center of the 
sun's motion. But whether the earth be moving 
round the sun, or the sun round the earth, or both 
about some other point in the line joining them, their 
apparent motion will be the same ; and as far as these 
two bodies only are concerned, we may consider the 
motion in that way which conduces most to clearness of 
explanation. So that just as we talk of the sun, moon, 
and stars rising and setting, though these are mere 
appearances, we may for the present speak of the sun's 
annual motion round the earth ; but when we have to 
consider the motion of another heavenly body relatively 
to the sun, we must transfer our thoughts to him, and 
picture to ourselves what the appearances would be 
from that point of view. No error is involved in eith- 
er way of speaking, provided we remember that we 
are only treating of relative motions. On this under- 
standing we will proceed to show how the apparent 
(or relative) motion of the sun gives rise to th 
sons. 

At the vernal equinox the days and nights, as be- 
fore stated, are equal, and this is the case all over the 
world, the equator being everywhere divided into two 
equal parts by the horizon. From this point the sun, 
moving along his oblique path, passes north of the 
equator, and two results follow from this, both of which 
cause places in the northern hemisphere to n 

* The arc corresponding to 1° at the center of a circle being 
5 fo of the whole circumference, which is '-'\ times the diame- 
ter, it follows that the length of the arc of 1° is gV of the 
radius nearly. 



THE SEASONS. 33 

more heat from the sun. In the first place the clay is 
lengthened and the night shortened, so that the time 
during which heat is received from the sun is increas- 
ed ; and in the second place the quantity of heat re- 
ceived in every hour is greater on account of the 
greater elevation of the sun, for his rays have a less 
thickness of the atmosphere to traverse and heat on 
their way, and further, a larger proportion of them 
strike a surface when they fall perpendicularly than 
when obliquely, just as in a driving shower a larger 
number of drops will fall on an umbrella when the 
stick is held in the direction of the shower than w T hen it 
is held upright. With regard to the loss of light and 
heat in passing through the atmosphere, it is sufficient 
to remark the enormous decrease in brightness of the 
sun near sunset to appreciate the influence of this 
cause, which reduces the sun's brightness at 5° eleva- 
tion to one-fifth of what it would be at the zenith. 
Now we must remember that the temperature of any 
body results from a series of exchanges with surround- 
ing bodies, heat heing received and at the same time 
sent out; hot bodies send out more heat than they re- 
ceive, and the reverse is the case with cool bodies. 
Now the earth receives a balance of heat from the 
sun; if it sends all this heat away into space all round 
it will remain in the same state as before, but if it re- 
ceive more than it can send away it will get hotter, 
and this is the case with places in the northern hemi- 
sphere at the time we are considering; for, as we have 
seen, such places receive more heat from the sun in 
the day, and have less time in the night to send it 
away and thus cool down, than was the case when the 
sun was at the equinox. But the quantity of heat 
received by the whole earth and sent out into space 
remains the same, for in southern latitudes the sun is 
below the equator (the north pole being below), and 
the days are shorter than the nights, so that those 
countries get cooler than they were at the vernal 
equinox. Now these opposite effects in opposite 
hemispheres go on increasing as ftie sun gets further 



34 THE SEASONS. 

and further north, till June 21; the northern hemi- 
sphere has by that time stored up such an accumula- 
tion of heat in the soil itself, that it does not begin to 
grow cooler till some time after, just as a kettle taken 
off the fire will continue to boil on another part of the 
stove, though the heat there is not sufficient to set it 
boiling. But this heat from the soil will he gradually 
dissipated as the sun moves southwards in the autumn, 
and the weather will grow colder and colder in northern 
latitudes, the reverse taking place in the southern 
hemisphere. Such an accumulation of ice and snow 
will be formed in the northern hemisphere, in conse- 
quence of the abstraction of heat which then takes 
place, that the arrears will have to be cleared off after 
the winter solstice, before the northerly motion of 
the sun produces any effect. 

Thus we may consider winter in the northern hemi- 
sphere (or summer in the southern) to correspond to the 
months of December, January, and February; spring 
(or autumn) to March, April, and May; summer (or 
winter) to June, July, August; and autumn (or spring) 
to September, October, and November. But there 
are certain portions of the earth where this division 
does not hold, viz., the regions near the equator. As 
the sun crosses the equator twice, he is vertical at 
such places twice in the year, and the same will be 
true for any place which is less than 231'' north or 
south of the equator, since for such places the celestial 
equator is less than 232-° from the zenith. The belt 
of the earth included between these circles of latitude 
is called the tropics, and since the heat at any place 
is greatest when the sun is vertical, these places have 
two summers; but really the change is very Blight, 
and the year is usually divided into the wet and the 
dry season, the term winter, as understood in our 
latitudes, being scarcely applicable. We may here 
allude to two other regions of the earth in which this 
word implies much more than it does with us. convey- 
ing 1 the idea of darkness as well as of cold, «»t' absence 
of light as well as heat. The sun at midwinter being 



THE SEASONS. 35 

23-J- below the equator, will not rise above the hori- 
zon of any place at which the celestial equator does 
uot reach an elevation of 23-^-°, which will be the case 
when the place is less than 23^° from either pole, or 
has a latitude (north or south) greater than 66^-°. 
The circles of latitude 66^-° north and south are called 
the Arctic and Antartic circles, respectively, and the 
belts included between them and the tropics are called 
the north and south temperate zones. In the Arctic 
and Antartic regions it is clear that the sun will in 
winter remain below the horizon during the whole 
time, that he is further below the equator than the 
distance of the place (in degrees) from the pole of the 
earth, and that he will in summer remain above the 
horizon for a similar period; so that the alternation of 
day and night is so far modified, that in summer we have 
sunlight continuously for weeks or even months at a 
time, and in winter we have a night of the same dur- 
ation. At the poles themselves these periods last for 
six months each, so that there is only one day and one 
night in the year, but of course the sun continues to 
circle round the pole once in every twenty-four hours 
just as in other latitudes, though, like the stars of the 
Great Bear with us, he never dips below the horizon. 
In this, as in many other cases, the ambiguity of the 
term day causes some confusion. 

We have already spoken of the effect of twilight in 
lengthening daylight; its influence is felt in a remark- 
able degree in polar regions, some light being receiv- 
ed from the sun in midwinter, even at places as near 
as 5° to the pole. 

Though, as has been already stated, it is perfectly 
legitimate to explain the alternation of the seasons, as 
has just been done, from the standpoint of the earth, 
yet, as the matter is of some importance, there will be 
advantage in considering it also from the point of view 
of the sun, which will enable us to realize more clearly 
some of the conditions on which these changes depend, 
and will at the same time remove any latent doubt as to 
the correctness of the conclusions based on a discussion 



36 THE SEASONS. 

of relative motions, a point of essential importance in 
the study of astronomy. We arrived at the conclusion 
that the earth moves round the sun in a plane orbit 
inclined to the equator, and that consequently the 
earth's axis is also inclined. Now this axis always 
points to the same place among the stars, very near the 
pole-star, constantly preserving the same direction 
during the year. Let us picture to ourselves, then, 
what would be the appearance presented to an inhab- 
itant of the sun by our globe during this annual motion. 
On a round (or slightly oval) table or tea-tray place a 
night-light a little out of the centre (in the direction of 
the longer axis of the oval) to represent the sun's light, 
and having run a straight piece of wire through the 
core of an orange, which will represent the earth and 
its axis, carry the orange round the edge of the table 
as the earth moves in the ecliptic, keeping the wire 
always tilted in the same direction; then if at the 
same time we keep the orange spinning pretty rapidly, 
the circumstances of the earth's motion will be repre- 
sented fairly well, and the flame of the night-light 
will not be far from the proportionate size of the sun, 
as compared with the earth's distance, though the earth 
ought to be represented by the minutest grain of sand 
visible to the naked eye, instead of by our orange. 
But our object being to explain the appearances pre- 
sented to an observer on the sun, we must suppose 
our earth magnified some 1,500 times, as if seen 
through an exceedingly powerful telescope. The 
figure represents the arrangement described above, 
seen from one side, the wire being omitted. 

Starting, as before, with the vernal equinox (at the 
top of the picture), when the sun appears to us on 
the equator, an observer on the sun will look at the 
earth's equator edgeways, and will just catch sight of 
both poles. As the earth moves on in her orbit, the 
equator, keeping always the same direction in space, 
will show its north side more and more to the sun, 
until it gets into such a position that all the tilt (south- 
wards) is in the direction passing through the sun, 



THE SEASONS. 37 

which corresponds to the solstice (the left of thefigure), 
after which less and less of the tilt is in the sun's di- 
rection, till at length, at the autumnal equinox, the 
equator is again presented edgeways to the sun (bot- 
tom of our figure). During this period the north pole 
is turned towards the sun, and the northern hemi- 
sphere receives more than its fair share of light and 
heat, as will be seen by noticing where the boundary 
of shadow falls on our orange illumined by the night- 
light. From the autumnal to the vernal equinox the 
tilt of the earth's equator, as seen from the sun, will 
be northwards, and therefore the north pole will be 
turned away and so receive less light and heat than 
the south pole, which is presented to the sun. It is, 




therefore, winter for the northern hemisphere and 
summer for the southern. We see at once from this 
that it is only the distribution of light and heat which 
varies from this cause, not the total amount. Some- 
times the northern hemisphere receives more than 
the southern, and sometimes the reverse is the case, 
but this does not affect the common fund. As a 
matter of fact, the earth does receive more light 
and heat in January than in July, but this is because 



88 PHYSICAL CONSTITUTION OF THE SUN. 

she is nearer the sun at the former epoch; the effect 
o/ this on the climate is, however, insensible, being 
masked by the.veiy much greater changes of the seasons. 
It is now time to pay a little attention to the physical 
constitution of that wonderful body which produces 
effects of such importance to our well being. When 
examined in a powerful telescope, care being taken to 
diminish the intensity of his heat and light by means 
of dark glasses, the sun appears to have a slightly 
mottled surface, shading off slightly towards the edge, 
and having usually certain dark markings, called spots, 
accompanied by streaks brighter than the ordinary 
surface, and hence called faculae (torches). If one of 
these spots be watched from day to day, it will be seen 
to move across the sun's disc, from east to west, disap- 
pearing at the western edge or limb only to reappear 
after an interval of nearly 14 days at the eastern limb, 
and cross the sun's face again in another 13 orl-i days. 
On extending our observations, it is found that all spots 
move across the sun's disc in about the same time, 
although the lengths of their path differ considerably, 
and we are therefore led to conclude that their motion 
is really caused by the sun's turning round on an axis 
eastward, or in the same direction as the earth in her 
orbit, so that it presents the same face to the earth 
again after an interval of some 27 days. But this is 
not the true time of rotation of the sun, for the earth 
having gone a little way round the sun in its orbit, 
the sun has to turn through a corresponding angle 
after having completed its rotation, so as to catch the 
earth up, just as we saw the earth had to do to bring 
the sun to the meridian of a place again. Now, as the 
earth goes round the sun in 365 days, we have, since 
the times are proportional to the angles turned through, 
3G5 -f- 27 : 365 : : 27 : time of sun's rotation which, 
therefore, is rather more than 25 days. As the result 
of careful measures of the position of spots during 
their passage across the disc, it is found that they do 
not move in straight lines except about July 1".' and 
December 11, showing that the circles which they de- 



ROTATION OF THE SUN. 39 

scribe, and therefore also the sun's equator, are tilted 
with respect to the ecliptic, the plane in which the 
spectator is, but that we see these circles edgeways 
(from opposite sides) on the two days given above, just 
as the equator and circles of latitude on the earth, 
(which are the diurnal paths of spots on the earth) 
would be seen from the sun at the vernal and autumnal 
equinoxes. The tilt of the sun's equator to the eclip- 
tic appears to be about 7i°. Now in all this we have 
something very similar to what we were led to conclude 
in the case of the earth, and thus the great difficulty 
of accepting the rapid motion of a mass like the earth 
is completely removed, for though the sun's rotation 
is much slower, yet its mass is enormously greater. It 
is difficult, indeed, to realize the size of this eriormous 
globe, but some assistance may be gained from the 
statement that a spot on the sun's equator moves four 
times as fast as a point on the earth's equator — i. e., at 
the rate of 4,000 miles an hour, which is five times the 
speed of sound, and four times that of a cannon ball 
— and that with this enormous velocity it takes 25 
days to complete the circuit of the sun. But though 
we have every reason to suppose that the spots turn 
round with the sun, the changes that take place in 
them show that they are by no means fixtures on his 
surface, and in fact it is found that one spot has a drift 
forwards relatively to another, so that they do not all 
take exactly the same time to go round. Their in- 
dividual movements, however, are small as compared 
with the motion caused by the sun's rotation, whilst 
the changes in their form are most remarkable. Cases 
have been observed of the formation of a large spot, 
some 50,000 miles across (six times the size of the 
earth), in the course of a single day at a part of the 
surface where nothing unusual was to be seen before ; 
and the disappearance is sometimes equally sudden. 
Usually a spot does not last more than two or three 
months, and in this period it will often break up into a 
group of smaller spots, or such a group may coalesce 
into one large spot. As a general rule, spots are com- 



40 fiOLAR PROMINENCES. 

posed of a central black portion, which is called the 
nucleus or umbra (shade), surrounded by a less dark 
part called the penumbra (half-shade), and these two 
portions are quite distinct, the nucleus lying at a low- 
er level than the penumbra, and both of them below the 
bright surface which we see ordinarily. That a spot 
must thus be considered as a hole in the luminous 
atmosphere of the sun, is shown by the appearance 
presented on its approach to the limb. We are then 
looking at the spot obliquely, and it is found that more 
of the penumbra is seen on the side away from us, 
whilst on the other side it is very much foreshortened, 
as we should expect on the supposition that the spot is 
a hollow with the nucleus at the bottom. An earthen- 
ware basin with a little inky water at the bottom will 
give a rough idea of the appearances thus presented 
by a spot. Of the causes which give rise to sun spots 
little is known, but they appear to be much more fre- 
quent about every eleven years, and there is a suspi- 
cion that this is due to the influence of the planets. 
We must now turn to some other features of the 
sun, the red cloud-like prominences, which are 
when the overpowering light of his disc i- cut off by 
the interposition of an opaque body like the moon, in 
total eclipses of the sun, and also by means of a 
beautiful application of the spectroscope, an instru- 
ment designed to determine the nature of the light 
which comes to us from any bright body. We will 
briefly explain tiie principle on which this i> founded. 
Everybody has noticed the colors shown by ;i 
lustre from a chandelier, and has probably rema 
that these colors change as the eve is moved. These 
effects will be best seen if a lustre be i laced on its 
flat side on a narrow stand, at some distance from 
and above the flame of a candle, and be viewed 
by an eye as far off as convenient. The first thing that 
will be noticed is, that the ravs from the candle are 
bent in passing through the glass, so that in or 
see the candle through it, it is necessary for the eye to 
be placed considerably below the stand. This property 



SPECTROSCOPE. 41 

of the glass is termed refraction (breaking), and is 
possessed in a greater or less degree by all transparent 
substances ; it is best seen when the glass is in the 
shape of a lustre, L e., a triangular bar, or prism, as it 
is technically termed. The next thing to be remarked 
is, that the flame no longer appears white, but is of a 
color which depends on the height of the eye, chang- 
ing from red to yellow, green, blue, and finally violet, 
as the head is lowered from the position at which the 
flame first begins to be seen in the prism. Thus it 
appears that the white light Of the candle is really 
composed of light of all the colors of the rainbow 
(a phenomenon caused by a somewhat similar action 
of the drops of rain on the light of the sun), and 
that it may be separated into these colors by a prism 
of glass which bends the violet rays most out of their 
course and the red least, the other rays lying between 
these two. When white light is thus spread out into 
its component co!ors, it is said to form a spectrum, 
and it is to be remarked that though for convenience 
of explanation we have spoken of red, yellow, green, 
etc., there is no sharp boundary between two contigu- 
ous colors, but that they shade insensibly one into 
the other, and that corresponding to every degree of 
bending or deviation there is a certain hue. Now 
though sunlight, or the light of a candle or gas flame, 
may thus be spread out into a continuous spectrum, 
the same is not true of every light ; thus burning hy- 
drogen gives out three definite kinds of rays only, cor- 
responding to definite hues of red, greenish blue, and 
violet. The prominences of the sun are found to give 
out light of these three hues exactly (indicating that thej 
also are glowing hydrogen). It is evident that the in- 
tensity of the light must be very much enfeebled by the 
spreading out into a continuous spectrum, or dispersion 
as it is called, an effect which may be doubled by put- 
ting another prism to receive the light after it has passed 
through the first, so that by making the rays go through 
a number of prisms one after the other, even the direct 
light of the sun may be made quite faint, whilst the 



42 MODE OF VIEWING PROMINENCES. 

light of the prominences is scarcely affected, since it 
consists of three definite hues, each of which is incapable 
of being spread out. The light which falls on the prisms 
is usually limited by a narrow slit (perpendicular to 
the length of the spectrum), and lenses are placed just 
in front of the first prism, and just after the last, 
so that the rays of each color form at a certain dis- 
tance an image of the slit of this particular hue, and 
having a corresponding position in the spectrum, which 
thus appears like a ribbon of shaded colors to an eye 
placed in a suitable position, and armed with a magnify- 
ing lens. Such an instrument is called a spectroscope. 
If now an image of the sun be formed on the slit of a 
spectroscope by means of a large lens, placed so that the 
slit is directly between it and the first prism, a red i mage 
of the prominences will be seen in the corresponding 
part of the spectrum, when the slit is so placed that it 
is just outside the sun's limb, the light of the sky close 
to the sun,though bright enough to blot out the prom- 
inences when viewed directly, being greatly enfeebled 
by dispersion into a continuous spectrum. In the same 
way we may see the prominences by means of the 
greenish-blue or by means of the violet light which they 
emit, if we look at those parts of the spectrum, respec- 
tively. There is thus found to be, outside the surface 
of the sun ordinarily visible to us, and known as the 
photosphere (or sphere of light), a layer of glowing 
hydrogen, to which the name chromosphi r< (sphere of 
color) is given from its red hue, and out of this rise 
strange cloudy masses, sometimes to a height of 80,000 
miles, or ten times the diameter of the earth. The 
chromosphere itself is on the average some 8,000 miles 
thick, but the thickness varies very much, as its surface 
is almost always in a state of great agitation, which, 
when very violent, gives rise to a prominence.. Besides 
hydrogen, there are, in its lower strata, the vapors of 
many of the metals, of which the presence is revealed in 
the spectroscope by the characteristic hues of which 
their light is composed, just as in the case of hydrogen, 
the hue being determined accurately by the position in 



CORONA— ZODIACAL LIGHT. 48 

the spectrum of the corresponding image of the slit, 
which will be a bright line of that hue stretching across 
the spectrum. There is another appendage of the sun 
outside the region of prominences which, so far, has 
only been seen in total eclipses, and which appears on 
the evidence of the spectroscope to consist chiefly of 
some substance not yet found on our earth. It extends 
to an enormous distance from the sun's surface, per- 
haps more than a million miles, and appears to be com- 
posed of two portions, the term corona being applied 
to the whole phenomenon from its resemblance to the 
corona or glory which is frequently seen round the moon 
in a hazy sky. The lower portion forms an atmosphere 
round the sun, visible as a ring of pale green, and 
appears to contain hydrogen as well as the unknown 
substance referred to above ; outside this are seen long 
rays and interlacing plumes, which can be traced to a 
distance of twice the sun's diameter, with large rifts or 
gaps reaching nearly down to his limb. This portion 
appears to shine partly by its own light, and partly by 
reflected sunlight. 

From this account it will be seen that the sun is made 
up of a large number of layers, there being below the 
photosphere, or luminous surface, two or possibly three 
layers which are exposed to view as the nucleus and 
penumbra of a spot; and above it the chromosphere, the 
atmosphere or inner corona, and the outer corona. 
Besides these there would seem to be a far larger ap- 
pendage of the sun, which is seen under favorable 
conditions (chiefly in the tropics) after sunset, or before 
sunrise, as a cone of light in the plane of the ecliptic, 
having the sun's place as its base. This is called the 
zodiacal light, and is now supposed to be composed of 
myriads of small particles which reflect the sun's light, 
and form a lens-shaped disc reaching probably beyond 
the earth's orbit. 

Of the cause of the sun's light and heat, both of 
which appear to come almost entirely from the photo- 
sphere, no satisfactory explanation has yet been given, 
and this remains one the most important subjects of 



44 APPARENT MOTION OF THE MOON. 

inquiry, the sun's rays being the immediate source of 
almost all movements that take place on the surface 
of the earth, or in its atmosphere. 



CHAPTER III. 

• The moon, as will be seen shortly, plays a very insig- 
nificant part in the solar system, but, next to the sun, 
it is, from its comparative proximity, the heavenly body 
of most importance to us. Its motion among the surs 
is somewhat like that of the sun, but far more rapid 
and far more irregular, the moon taking 27^ and 29£ 
days to return to the same position nearly with i • 
to the stars and the sun respectively, the latter period 
being longer on account of the sun's apparent motion 
(or the earth's real motion) in the interval, since the 
moon has to overtake the sun, which is traveling more 
slowly in the same direction. The former is called a 
siderial, and the latter a synodic period or lunation. 
The determination of the moon's motion is afar more 
complicated question than that of the sun's, but by 
watching its course among the stars, which can be done 
much more readily than in the case of the sun, as moon- 
light is not sufficient to overpower them, it will be 
fqund that the moon moves in an orbit tilted about 
5° to the ecliptic or apparent path of the sun, the 
arc described in a day varying from about 14J° to 12°. 
while the diameter changes from 29^' to 3'2j\ showing 
that the moon's distance alters by about one-ninth 
part. It thus appears that the moon seems to describe 
the same sort of a path about the earth as the sun 
docs, but its ellipse is much more oval ; it will fur- 
ther appear that the moon is much smaller than the 
earth, so that it is natural to suppose that it really re- 
volves round the earth, and not the earth round the 
moon. But further observation soon shows 1 hat the 
in- urn's motion is not quite so simple as this explanation 
would lead us to suppose, though it represents the broad 



IRREGULARITIES IN THE MOON'S MOTION. 45 

facts of the case, and is a fair approximation to the truth. 
In the first place, it will be found that when the moon 
comes back to the ecliptic after having made the tour of 
the heavens, it does not return to exactly the same place 
on that great circle, but that the point where it crosses 
is nearly 1^° further west, so that ths moon's motion 
is not really in a plane. It will, however, give us a . 
clearer notion of the path if, instead of supposing the 
moon to depart from the original plane, we imagine 
this plane to be continually shifted so as to follow, as 
it were, the moon's movement exactly, the moon being 
then always in this shifting plane, which may thus in 
some sense be considered the plane of its orbit, and 
this will, at any rate, assist us in realizing what the 
motion actually is. Looking^upon this, then, merely 
as a r device to assist us in grasping a difficult subject, we 
may say that the moon moves in a plane, inclined about 
5° to the ecliptic, and twisting round without altering its 
tilt at the rate of l-J-° westward in every lunation, so 
that it has twisted completely round in 18f years.* 
Again, when the moon is observed through several 
lunations, the point where she is nearest to us, and 
where her daily motion is greatest, is found to shift 
eastward by about 3° in every lunation, so that the 
moon does not really describe a closed curve, such as a 
circle or ellipse, though for the reason given above it is 
convenient to speak of her as moving in an ellipse (or 
oval), which is continually turning round eastward at 
the rate of 3° every lunation, completing a circuit 
within nine years. There are other irregularities which 
make it necessary to suppose the size and shape of this 
ellipse variable ; so that the moon's distance from us 
changes by more than one-ninth when different 

* The plane of the moon's path may at any instant be deter- 
mined by supposing: it tilted 5 cleg, to the ecliptic about a hinge, 
as it were. The direction of this hinge is called the line of 
nodes (see fig. p. 64), the nodes being the points where the 
moon's apparent path in the heavens crosses the ecliptic. The 
line of nodes then shifts 1 deg. westward every lunation, 
going completely round once every 18f years. 



46 LONGITUDE FOUND BY MOON'S MOTION. 

lunations are compared, the apparent diameters 
ranging from 29^- ' to 33^ ' . It may be asked — What 
is the use of supposing the moon to move in an ellipse 
when we have to make continual alterations in its 
positions and dimensions ? But, in answer to this, it 
must be remembered that these alterations are small, 
and that by this way of looking at the subject we are 
able to consider the irregularities one at a time, 
instead of being overwhelmed by their mere number. 
It is by this mode of considering the question that t*he 
lunar theory, which from a study of the moon's 
motions aims at predicting her place at any future 
time, has been brought to a high state of perfection, 
a matter of the greatest practical importance to 
navigation, as the moon's somewhat rapid motion 
among the stars enables us at any place to determine 
the Greenwich or Washington time within a few 
seconds by measuring her distance from certain 
selected stars, and in this way to determine the 
longitude (which, as already explained, is simply tie 
difference between the time of the place and Wash- 
ington time), thus fixing a ship's position at sea 
within a very few miles. In fact the moon serves the 
purpose of the hand of a clock which always shows 
Washington time, though the marks corresponding to 
the minutes are not at equal distances ; and the great 
object of the lunar theory is to tell us where these 
minute marks are to be, in order that the moon 
shall aways point to true Washington time. It is as 
if, when a clock went wrong from irregularity in its 
movements, we were unable to alter the hands, and 
had to make new marks on the dial in order to know 
the correct time. This question was considered one 
of such great national importance that the Royal 
Observatory, Greenwich, was founded by Charles II, 
in 1G75, for the express purpose of Matching the 
moon's motions; and though careful observations have 
been made there assiduously for the last 130 years, and 
at other observatories, there are still slight errors in the 
predicted places of the moon, though these are of much 



PHASES OF THE MOON. ' 47 

smaller amount than the uncertainty of measures of 
the moon's distance from stars made at sea. 

It is now time to give an explanation of the most 
striking peculiarity of the moon — her phases. The 
sun always appears as a round orb, but not so the 
moon. Starting from new moon, when she is in con- 
junction* with the sun, the first appearance presented 
by the young moon, a day or two afterwards, is that 
of a thin crescent, of which the hollow is turned away 
from the sun ; the thickness of this crescent gradually 
increases till it becomes a half-circle at first quarter, 
when the moon is 90° from the sun ; from this point 
the contour of the side away from the sun becomes 
more and more convex, till, when the moon is almost 
exactly opposite the sun at full moon, we see a nearly 
complete circle of light, a very small part of the top 
or bottom only being wanting, according as she is 
(from the tilt of her path) below or above the point 
exactly opposite the sun. After this the west side 
begins to wane, and at last quarter we have again 
a half-circle, but with the round side towards the east, 
the sun being now on that side ; the crescent form 
now appears again, becoming thinner and thinner as 
new moon approaches. Thus from last quarter to 
first quarter the moon is crescent-shaped, whilst from 
first quarter to last quarter she is said to be gib- 
bous, the point to be noticed being that a full circle of 
light is seen when the sun is opposite her, whilst we 
see little or nothing when they are nearly in the same 
direction. This suggests the idea that the light of 
the full moon is due to the sun shining directly on 
her, and that the reason we see nothing at new moon 
is that we are then looking at the dark side, the moon 
being between us and the sun. In fact the phases 
are exactly what we should see in the case of the 
sun shining on a dark globe, as may readily be 

* One heavenly body is said to be in conjunction with another 
when it has the same longitude, or right ascension, i. e., when 
it is either in a direct line with the other, or due north or south 
of it. 



48 



THEIR CAUSE. 



verified by holding a white ball at arm's length 
between the eye and the sun or a light, and slowly 
turning round with it from right to left. Care being 
taken that there be no other lights to interfere, it will 
be found that the ball is always divided into two 
halves, a bright side turned to the light and a dark 



LAST.pUA/trS/t. 




FIRST. QUARTER. 

LAST puwrrit 



l FULL 



U3Wnq JSWJ 
PHASES OF THE MOON. 

In the upper figure a bird's-eye view of tin" 1 earth and moon 
in different parts of her orbit is given, the horizontal lines 
showing the direction in which the smi's light falls : the 
eafth and moon are each of 12 times their proper rise ;i> 
compared with the orbit. The Lower figure shows n 
responding phases of the moon — the lower part, from new 
to full, is to be looked at upside down. 



EARTH LIGHT— OCCULT ATIONS. 49 

side turned away, and as the ball goes round us, more 
and more of the bright side comes into view, till at 
last the whole of it is seen ; after this the bright side 
turns away, and we lose it altogether when the ball 
comes again to its position between us and the light. 
It will be noticed that the edge of the ball turned to 
the light is bright, whilst the opposite edge is dark, 
and therefore not well seen, and this is just the case 
with the moon, the deficient part required to make up 
the circle being always away from the sun ; but that 
it really exists, though on account of the overpower- 
ing light of the bright portion we generally cannot 
see it, is shown by the fact that near new moon, 
when the light of the thin crescent is comparatively 
faint, we can readily trace the outline of the whole 
disc against the sky. There is another circumstance 
too which contributes to the visibility of the dark 
portion at such times, viz., that this part of the moon 
is illuminated by the light reflected from the earth, 
just as the part of the earth turned away from the 
sun is by the full moon ; for when it is new moon 
to us it is full earth to the moon, and vice versa, and 
the earth being, as we shall see, four times the size 
of the moon, earthlightto the moon will be something 
like sixteen times as bright as moonlight is to us, that 
is, supposing the reflecting powers of the bodies to be 
about the same, as is probably the case. But besides 
this appearance of the new moon with the old one 
in her arms, as it is called, we have direct evidence of 
the existence of the dark part of the moon, when we 
cannot see it, in eclipses of the sun, and in occulta- 
tions of stars. To take the latter first. It is clear 
that when the moon passes between us and the 
stars (which are at an enormous distance from us) 
she will cut off their light, so that any star placed 
in the moon's course will be hidden or occulted 
when the moon passes over it, and this disappear- 
ance will, before full moon, take place as soon as 
the eastern or dark part of the moon's circle comes 
up to the star showing that an opaque body having 
4 



50 ECLIPSES OF THE SUN. 

this circular outline is interposed between the star and 
us ; similarly after full moon the star does not reap- 
pear till it reaches the western edge of the same circle, 
the bright part being now to the east. It may be re- 
marked here that these occultations of stars afford the 
most accurate means of determining longitudes where 
the telegraph is not available, the disappearance or 
reappearance taking place quite instantaneously, bo 
that the observation may be relied on to a fraction of 
a second of time. As the plane of the moon's orbit 
shifts regularly round once in 18f years, it is evident 
that in that period the moon will have occulted at 
some time or other every star which lies within 5° on 
either side of the ecliptic, and will consequently, oc- 
casionally pass in front of the sun, causing an eclipse. 
This will happen whenever new moon takes place 
near the points where the moon's path cuts the ecliptic 
(the moon's nodes) ; in other cases the moon will pass 
above or below the sun, being tilted out of the ecliptic. 
If the new moon takes place exactly at the node she 
will pass centrally over the sun, and the apparent 
diameters of the two bodies being on the average about 
equal, but each subject to variation through alteration 
in the distance from us, especially in the case of the 
moon, we shall at some central eclipses have the whole 
of the sun's light cut off for a few minutes (a total 
eclipse), and at other eclipses (known as annular) there 
will be seen just at the middle of the eclipse a ring of 
light from the sun round a black circular disc (the 
moon). If the moon when new be not exactly in her 
node, more or less of the sun's disc will be cut off, and 
a partial eclipse will take place ; such an eclipse will 
happen when the moon's centre appears to pass within 
the distance of her radius from the sun's edge, which 
will be the case when the angular distance from the 
node is not greater than 17 J , or when the pae 
across the ecliptic is not more than about 1J days from 
new moon. But though an eclipse will, under these 
circumstances, occur at some place or other on the earth, 
eclipses at any particular locality are not so common, 



ECLIPSES OF THE MOON. 51 

and total or annular eclipses are exceedingly rare, for 
a change in the position of a spectator on the earth will 
throw the moon out of the direct line between him and 
the sun, and thus prevent the sun from being eclipsed 
at one place when it is so at another a little north or 
south of it. There will be no total eclipse visible in 
England during the remainder of this century, the next 
being in a. d. 1927. As the moon sometimes cuts off 
the sun's light from us, so the earth may cut off the 
sun from the moon; when an eclipse of the moon, as 
we call it, takes place, the appearance being that of 
the moon passing into the earth's shadow, and so dis- 
appearing, more or less completely, through the sun's 
light being cut off; except in so far as it is scattered 
by clouds in our atmosphere, owing to which effect the 
eclipsed moon is usually seen as a dark copper-colored 
disc. The moon's shadow barely reaches to the earth 
in an eclipse of the sun, and under the most favorable 
circumstances, throws a black spot on the earth not 
more than 120 miles in diameter; but the earth being 
four times the siz.e of the moon, her shadow reaches 
far beyond the moon's orbit, and is at the distance of 
the moon about two-and-a-half times the moon's 
diameter. If the moon when full be near enough to 
her node to pass within this shadow, an eclipse will 
take place, and this will happen whenever the dis- 
tance from either node at opposition is less than lOf °, 
or when full moon occurs within 20 hours of the pas- 
sage across the ecliptic. Unlike an eclipse of the sun 
a lunar eclipse is visible at any place for which the 
moon is above the horizon, i. e., on the hemisphere 
turned towards the moon and away from the sun, the 
position of the spectator not affecting the entry of the 
moon into the earth's shadow. From the earliest times 
eclipses forced themselves on the attention of mankind, 
having in one notable instance (the eclipse predicted by 
Thales) put an end to a war between the Medes and 
Lydians, as related by Herodotus, so that a method 
of predicting them was eagerly sought for. If only a 
cycle of years could be found, such that eclipses would 




ECLIPSES OF MOON AND BUN. 

The sun ought to be removed to nearly 400 times the dis- 
tance m e, and to be 2% times as large. The earth and moon 
are 12 times their proper size. 
52 



CYCLE OF ECLIPSES-GOLDEN NUMBER. 53 

recur in the same order in each successive cycle, the 
question would be easy enough. Now, two conditions 
are necessary for an eclipse : — (1) The moon's node 
must be near the sun's place ; (2) The moon must be 
new for a solar, or full for a lunar eclipse. If, then, 
after one eclipse the node has completed an exact 
number of revolutions with regard to the sun so as to 
return to the same place again, whilst in the same 
time an exact number of lunations has elapsed so that 
the moon is again new or full, as the case may be, 
another eclipse will happen under precisely similar 
conditions. The Chaldeans discovered such a period, 
which they called the Saros, a cycle of 18 years and 
11 days, in which the node has made 19 revolutions 
with respect to the sun, which differ from 223 luna- 
tions by only 11 hours in excess. Thus, if an eclipse 
happens at any particular date, it will recur after 18 
years and 11 days, and this will go on till the node is 
thrown beyond the limit for an eclipse by the accumu- 
lation of the lagging in 11 hours for each cycle ; an • 
eclipse of the sun will recur in this way at intervals 
of 18 years and 11 days for some 1,000 years, and one 
of the moon for about 800 years before the lagging 
of the node interferes with its regularity. 

There is another cycle connected with the moon 
which is of some interest, as it gives the days on which 
new moon falls. It is called the Metonic cycle, from 
the name of its discoverer, Meton, and consists of 19 
years, corresponding almost exactly to 235 lunations, 
so that the days of the month on which new moon 
falls recur regularly after this interval ; the number 
which denotes the position of a year in this cycle is 
called the Golden Number. 

A consequence of the moon's moving in a path in- 
clined to the equator may here be noticed, as it is of 
some importance to the farmer. From the tilt of the 
ecliptic the moon's motion in her orbit is inclined to 
the equator, and is partly eastward and partly north or 
south. When she is in that part of the ecliptic where 
the sun is at the vernal equinox, her motion north- 
wards is most rapid, and in high northern latitudes is 



54 HARVEST MOON— PARALLAX. 

nearly parallel to the horizon, so that her motion east- 
wards, which tends to make her rise later, is compen- 
sated by the northward part of her motion, and con- 
sequently she will in that part of her path rise at 
nearly the same time on two or three successive nights, 
and this will happen once in every lunation. There 
is a special importance, however, in this phenomenon, 
when the full moon falls at this part of the orbit, for 
then the moon rises for several days just at sunset, 
and thus gives light enough to get in the harvest, 
whence this is called the Harvest Moon. As in this 
case, the moon is full at the vernal equinox, the sun, 
which is exactly opposite, must be at the autumnal 
equinox, so that the harvest moon is that full moon 
which is nearest to September 22. In England and 
the United States the harvest is usually over some 
weeks before this, but in many countries this length- 
ening of the day by the harvest moon is of great 
value. 

The moon's distance from the earth has been very 
accurately determined by a method founded on the 
fact that as an observer moves forwards, objects on 
either side of him appear to move backwards with a 
rapidity proportional to their distances from him, an 
effect which is well seen from a railway carriage in 
motion, the trees and houses in the landscape appear- 
ing to wheel about a point in the extreme distance on 
either side as a pivot. For every yard that the train 
advances every object will appear to move a yard back- 
wards, so that each object is shifted apparently through 
the angle subtended by a yard at the distance of the 
object, which explains the slower apparent motion of 
the more distant objects. By measuring, then, the 
angular shift of any object, we determine the angle 
under which a yard appears at the distance of that 
object, and hence readily the distance itself. For an 
arc of 5 7 A is equal to the radius of the circh* (the 
circumference of 300° being o\ times the diameter), 
whence we have only to divide the angle we measure 
into 57i 3 <j° to find how many times the radius contains 



DISTANCE OF THE MOON. 55 

the arc, which, in the case we are considering, is one 
yard; the number of times so 'found will, of course, 
give the distance in yards. It is not necessary that 
the spectator move in an arc of a circle about the 
object as a centre, for in dealing with small angles the 
arc is very nearly a straight line, and the difference 
is easily allowed for where accurate calculutions are 
made. 

Now let us apply this principle to the case of the 
moon, remembering that the distances we are here 
concerned with are very large, and that we have to 
deal with thousands of miles in the place of yards. 
Suppose two spectators at the extreme north and south 
of the hemisphere visible to the moon, which is, there- 
fore, on the south horizon in the one case and on the 
north horizon in the other. The southern observer 
will see the moon shifted north among the stars (which 
are too far off to be so affected) through an angle equal 
to the angular diameter of the earth seen from the 
moon, and the part that this angle is of 57tV gives the 
fraction that the earth's diameter is of the distance of 
the moon, so that, having the diameter of the earth, the 
moon's distance is easily found in miles. But in prac- 
tice it would not be very easy to make observations at 
two such stations as we have supposed, and it is found 
better to be satisfied with a rather less shift in order 
to have the moon at a sufficient altitude at both stations 
to get rid of the uncertainties of refraction near the 
horizon. The observatories which have been used for 
this purpose are those of Greenwich and the Cape of 
Good Hope, at both of which the moon is observed with 
the utmost regularity every day that she is visible; so 
that a large number of observations are available, the 
average of which will give a very accurate result. 
The mode of determining the moon's distance by ob- 
servations at these two stations is not quite so simple 
as in the ideal case given above, but the matter may 
be made clear by the following consideration. From 
every point of the earth's surface the moon is seen in a 
different position, so that by plotting down correspond- 



56 EQUATORIAL HORIZONTAL PARALLAX. 

ing places of the moon's center amoDg the stars, we 
shall have a representation of the points of the earth's 
surface as seen from the moon, the apparent shift of 
the moon from its central position being, as already 
stated, equal to the apparent distance of the corres- 
ponding station from the centre of the earth's disc as 
seen from the moon : this is called the moon's paral- 
lax, being the difference between her direction as seen 
at the given place and at the earth's center, and is 
evidently greater for points round the edge of the 
earth's disc than for those within : for the former the 




PARALLAX OF THE MOON. 

The left hand figures show the position of the moon as 
seen from five stations on the earth ; the lower figures give 
the earth's disc seen from the moon and the i mag nary di so 
marked out by the moon as seen from different places of the 
earth ; but reversed right for left, as if looked at from out- 
side a celestial globe. 

moon is at the given instant on the horizon, and the 
shift of her apparent position is then called horizontal 
parallax. The earth's disc as seen from the moon not 
being perfectly circular on account of the bulging our 
of the equator, the horizontal parallax will be greatest 
at the equator, since the two points where the equator 
meets the edge of the disc are further from the center 
than any others ; this value is called the Equatorial 
Horizontal Parallax. It will, of course, be understood 
that on account of the earth's rotation the disc visible 



METHOD OF FINDING MOON'S PARALLAX. 57 

to the moon is continually changing, and that, conse- 
quently, the parallax at any place changes as the moon 
rises or sets. The moon being in the zenith of the 
place at the centre of the disc, the parallax is nothing 
for that position of the moon, and increases as she 
moves toward the horizon. Now when the moon 
is on the meridian of Greenwich, it is easy, from her 
observed zenith distance, to calculate what part the 
apparent distance of Greenwich from the middle of 
the earth's disc, as seen from the moon, is of the di- 
ameter of that disc, and, again, when the moon is on 
the meridian of the Cape Observatory, the correspond- 
ing fraction in that case ; so that by adding these 
two fractions together, the proportion of the apparent 
shift in the case of Greenwich and the Cape to the shift 
for the two extremities of a diameter is obtained. 
The shift corresponding to Greenwich and the Cape is 
obtained by observing the moon's meridian distance, as 
compared with those of selected stars at both observa- 
tories, or, in other words, the shift of the moon with 
respect to stars near, allowance being made for the 
moon's motion in declination in passing from the me- 
ridian of Greenwich to that of the Cape. In this way 
it is found that the shift for two extremities of an 
equatorial diameter is 1° 54', which is, therefore, the 
diameter of the earth's disc at the moon's average dis- 
tance ; so that the equatorial horizontal parallax is 
57'. The moon's distance is, therefore (since 57t 3 <t° is 
about 60 times 57'), about 60 times the earth's radius 
at the equator, or 30 times its diameter, making it 
about 239,000 miles. Since the moon's apparent di- 
ameter at her mean distance is about 31', while that 
of the earth is 1° 54', it follows that the real diameter 
of the moon is rather more than one-fourth that of the 
earth, being very nearly 2,160 miles. We may now 
get a tolerably clear idea of the motion of the moon 
about the sun, for we see that while she is moving 
round the earth at a distance of 60 times the earth's 
radius in a lunar month, the earth is moving round the 
sun at 388 times this distance (23,400 times the 



58 MOTION OF MOON ROUND THE SUN. 

earth's radius) once a year, and carrying the moon 
with her. Thus if a circle, or more strictly an ellipse, 
be drawn of four inches radius to represent the path of 
the earth round the sun, the moon's motion round the 
sun will be represented by dividing the circumference 
into 13 parts about ; and supposing the moon at these 
13 points corresponding to new moon to be r U inch 
inside the middle of the line representing the circum- 
ference, and at intermediate points corresponding t<> 
full moon to be totj inch outside, so that the excursions 
of the moon will all be contained within the breadth 
of the pencil line which marks the circumference and 
the deviation of her path from a true circle (or nearly 
circular ellipse) about the sun would be quite unap- 
preciable to the eye on such a scale. It may seem 
strange that we should speak of the moon describing 
an ellipse round the earth when she really moves very 
nearly in a circle about the sun, but in explanation 
of the apparent anomaly it is sufficient to remark that 
the earth is dragging the moon with her round the 
sun at the rate of 18 miles a second, whilst the moon's 
motion round the earth is only i 6 u of a mile in the same 
time, so that even when the moon's motion round the 
earth is in the opposite direction to that in which she 
is carried by the earth's motion round the sun, which 
is the case at new moon, the moon is still moving 
round the sun in the same direction as the earth, and 
with a velocity only about & less. Thus we may con- 
sider the moon as describing either an ellipse about 
the earth or an almost circular oval about the sun, 
according as we take the earth or the sun as our stand- 
point ; both modes of expression arecorrect, provided 
we remember that the motion is in both cases relative, 
and that the sun itself may be moving round some 
tar distant centre one quarter as rapidly in space as 
the earth is round the sun, so that the earth and the 
moon too may really be describing nearly circular 
paths round this distant orb, a supposition which BOme 
astronomers consider probable. However this maybe, 
we can commit no error in considering the moon to 
move round the earth, and both earth and moon to 



ROTATION OF THE MOON. 59 

move round the sun in nearly circular paths, so long- 
as we confine ourselves to the relative motions of these 
three bodies, without reference to any real (as dis- 
tinguished from apparent) motions they may have 
among the stars. 

There is one peculiarity of the moon w T hich strikes 
every one who watches her disc through a tel- 
escope — it is this: she always presents the same face 
to the earth as she circulates round it. Now this can 
only arise from her turning round on her own axis in 
exactly the same time as she turns round the earth, 
though at first sight it may seem a little difficult to 
see how she can be really rotating, when she does not 
show any signs of it to us. A little consideration of 
what was said in the last chapter on the relative 
motion of two bodies will remove this difficulty. 
It was there pointed out that, as far as the two bodies 
are concerned, the appearances would be exactly the 
same to a spectator on either the earth or the sun, 
whether the earth went round the sun or the sun round 
the earth, and that so long as we were dealing with 
those two alone, it was only a question of conven- 
ience which expression we used. Now the same prin- 
ciple applies to the earth and moon ; so that so long 
as we are considering the moon's appearance to us, 
and not her motion among the stars, we shall have the 
same result by supposing the earth to be moving round 
the mcon, as in the actual case. But if the earth be 
turning round the moon, it is evident that, for the 
same face to be always seen by the earth, the moon 
must turn on her own axis exactly at the same rate 
as the earth turns round her, that is, once in 27-g-days. 
To represent the moon's motion round the earth, we 
must suppose the earth to turn round the moon some- 
times faster and sometimes slower, so that she is alter- 
nately in advance of and behind what we may call 
her proper place, just as in the case of the sun ; the 
moon, on the other hand, turns quite uniformly on her 
axis, and the earth in consequence gets to see a little 
more round one side at one time and a little more 



60 HER ASPECT— ABSENCE OF ATMOSPHERE. 

round the other side at another, through her out- 
stripping or lagging behind the moon in her turning. 

The moon being such a very near neighbor of ours, 
as compared with other heavenly bodies, her surface has 
been studied with great success by means of powerful 
telescopes, and careful charts have been made in which 
the positions of all the principal markings on her visible 
disc are laid down with an accuracy surpassing that of 
most terrestrial maps. With a magnifying power of 
500 the moon may, with a powerful telescope and ex- 
ceptionally clear state of our atmosphere, be brought 
apparently within about 500 miles, a distance at which 
the principal features of a country would readily be 
made out. Fortunately for the study of her surface she 
appears to be quite destitute of any appreciable atmos- 
phere, no trace of refraction being perceived when the 
rays from a star graze her surface just before an occul- 
tation, and no signs of water or vapor being visible on 
her disc. This absence of atmosphere exposes the moon 
to most violent changes of temperature, the surface 
being heated during the long lunar day of half a month 
to the melting point of iron, and cooled during the 
next fortnight to the temperature of space, or further 
below the freezing point than the boiling point of 
water is above it, a condition of things which would of 
course be fatal to any form of life with which we are 
acquainted. 

The moon's surface almost everywhere shows signs of 
violent volcanic action far exceeding anything found on 
the earth, the most conspicuous features being the cra- 
ters, which are found of all sizes, from eighty milefl 
down to the most minute speck visible, crowded to- 
gether so closely in many regions that they overlap each 
other. The great peculiarity of these lunar craters is that 
the floor inside is nearly always at a far lower level than 
the outside surface, as may be shown by measuring the 
lengths of the shadows cast by the rampart round the 
crater on the floor and on the surface of the moon out- 
side. From such measurements it is easy, when the 
elevation of the sun is found (from the angular distance 



LARGE SIZE OF CRATERS. 61 

of the crater from the illuminated edge) to determine 
the height of the rim of a crater or of a mountain, and in 
this way the altitudes of a large number of objects on 
the moon have been obtained. Although the moon is 
only a quarter the diameter of the earth, there are both 
craters and mountains rivaling in height the most 
elevated peaks on the earth ; nor is this to be wondered 
at, for we have no reason to suppose that the force of 
volcanic energy is less for a small planet ; whilst gravi- 
tation on the moon, which draws heavy bodies down- 
wards, and so counteracts the force of upheaval, is only 
a sixth of what it is on the earth ; so that we should ex- 
pect cinders to be projected from lunar volcanoes to a 
much greater distance than is the case on the earth, a 
supposition fully borne out by the large size of many 
of the craters on the moon. Though both craters and 
mountains are found on the moon, the former are far 
more frequent, there being only three principal rang' s 
of mountains, called respectively the Alps, <he 
Caucasus, and the Apennines, the moon in this respecc 
presenting a marked contrast to the earth. The 
mountain ranges are all three situated in the north, 
whilst the southern portion of the moon is remarkable 
for its large number of craters, the most conspicuous 
of which, Tycho, seems to form a centre of eruption, 
from which proceed in all directions bright rays, ex- 
tending in some cases to a distance of 600 miles. 
This crater is over fifty miles in breadth and some 
18,000 feet in depth, with a central cone 5,000 feet 
high, and with its system of radiating streaks is dis- 
tinctly visible to the naked eye about full moon. 
Similar systems of bright rays proceed from several 
other craters, among which may be mentioned Coper- 
nicus, which is well seen near the middle of the 
boundary of the bright part of the moon a day or two 
after the first quarter, and Aristarchus, which first 
comes into view as an exceedingly bright spot in the 
north-east two or three days before full moon. The 
first idea that suggests itself with reference to these 
rays is, that they are streams of lava flowing from the 



62 BRIGHT RAYS—PLAINS OX MOON. 

craters, but a fatal objection to this explanation is 
that they pursue their course over hill and dale, regard- 
less of the obstacles in their path, and can actually be 
traced across the floors of craters which must have 
been formed before this eruption, the way in which 
one crater overlaps another affording an indication of 
its relative age. The most plausible explanation offered 
as yet seems to be that the rays are cracks, like stars 
in ice, caused by the eruptive force which formed the 
crater, and covered over by the lava which has exuded 
from them, just as radiating streaks are formed in a 
sheet of ice by the freezing of water that comes 
through the cracks. It remains to mention the so- 
called seas on the moon, which are apparently nothing 
but dark grey plains composed of materials that reflect 
less light than other portions, and which from their 
size are sufficiently conspicuous to the naked eye, 
especially at full moon, when the markings present 
some resemblance to a human face. Though the 
term sea conveys a false impression of the nature of 
these plains, there being a total absence of water on 
the side of the moon turned towards us, the term is 
still retained to avoid the confusion which might be 
caused by introducing a new nomenclature, the "seas" 
being named from supposed qualities, e. t <7., Mare Im- 
brium, Mare Nubium, and the craters and mountains 
from celebrated philosophers. 



CHAPTER IV. 

Having discussed the motions of the sun and moon, 
we shall now be better prepared to study the far more 
complicated movements of the planets. Tin- planet 
Venus, which is so conspicuous as a morning or even- 
ing star at different parts of her course, will serve as 
the best introduction to the question. Suppose, then, 
we watch this planet when she first appears as an 



MOTION AND PHASES OF VENUS. 63 

evening star, setting soon after the sun ; it will be 
found that her angular distance from the sun increases 
day after day, till after seven months she arrives at a 
turning point nearly 47° from the sun, after which she 
begins to approach him again, and after another two 
months is again lost in his rays at sunset. All this 
time, if watched through a telescope, her diameter 
will appear to increase gradually to six times its orig- 
inal value, whilst she goes through phases like the 
moon, from nearly full when first seen, to a fine cres- 
cent at her disappearance in the evening twilight. 
After a short interval she may be again picked up, but 
this time as a morning star, just before sunrise, and 
continued watching will show that her distance west 
of the sun increases for nearly seven months, as her 
distance east did before, and that after reaching 47° 
it diminishes for the next two months, till she is again 
lost in the sun's rays, to reappear east of him, the phases 
and changes of diameter corresponding to those seen 
when she was an evening star. These movements 
may be watched more closely with a telescope, which 
enables us to see the planet in broad daylight if we 
know whereabouts to look ; the best way of fixing the 
position will be to observe with a transit-circle the 
time of transit, and the meridian altitude of the 
planet, the corresponding quantities being also deter- 
mined for the sun, so that the right ascensions and 
declinations of both bodies are found, and therefore 
their relative position. From a consideration of the 
motions above described, it appears that Venus moves 
in some way about the sun, never getting very far 
from him, and that she is more than six times as far 
from us when she changes from a morning to an 
evening star than in the opposite position. Again, 
her phases show that when nearest, or in inferior con- 
junction, she is between us and the sun, as the moon 
when new, whilst when furthest off, or in superior con- 
junction, she is beyond the sun, so that we see the side 
lighted up by him ; for, as in the case of the moon, we 
may conclude that Venus shines by light reflected 



64 ORBIT OF VENUS. 

from the sun, though she is never seen in the quarter 
of the heavens opposite to the sun, as is the case with 
the full moon. It follows from all this that Venus de- 
scribes a smaller orbit round the sun than the earth does, 
and that consequently she is always inside the earth's 
path ; the time she takes to complete a revolution with 
respect to the earth is 584 days, or 1£ years nearly, in 
Avhich period she must have made 2f revolutions 
relatively to the stars, having gained exactly one 
revolution on the earth ; so that the time of one 
sidereal revolution is found by dividing If years bv 2?, 
and is, therefore, A of a year, or about 224 days 
(more exactly 224.7 days), which is somewhat over 7 
months. The determination of the exact path 
described by Venus is a more complicated matter, 
since it is necessary to find from observations made on 
the earth her positions as seen from the sun; but when 
this is done it appears that, 
like the earth, she describes 
an ellipse round the sun, 
having a tilt of nearly 3^° 
to the earth's path. Since 
Venus is six times as far 
from us in superior conjunc- 
tion as at inferior, it follows 
that the diameter of her or- 
bit, which is the difference 

, 7 . ,. TILT OF ONE ORBIT TO ANOTHER 

between these two ais- showing line of nodes. 
tances, must be five times 

her least distance from us; so that her distance from 
the sun is about 2% times and the earth's distance is 
3-^ times the distance of Venus from us when near- 
est; thus her distance from the sun is 2-£ divided by 
3^-, or about 4 of the earth's distance from the sun. 
The same result may be arrived at by observing her 
greatest angular distance from the sun (or elongation 
as it is termed), in the same way as the breadth of a 
round tower may be found by observing the angle 
under which it appears at a known distance from its 
centre. We shall see presently how the relative dis- 




ORBIT OF ME ECU BY. 65 

tances of the planets may be determined more ac- 
curately indirectly by means of their times of revolu- 
tion, or years as they may be called. 

There is another planet, Mercury, whose motions 
are similar to those of Venus, though he is much closer 
to the sun, and can only be seen under favorable 
circumstances, when his angular distance is greatest, 
either as an evening or morning star. This planet 
goes through all its phases in four months ( nearly 116 
days) whence it follows, by the same reasoning as in 
the case of Venus, that its year is three months 
(more exactly 88 days); the distance from the sun 
varies more than is the case with Venus or the earth, 
Mercury's orbit being- much more oval. His distance 
from the sun is about § of that of the earth, subject to 
an increase or decrease of one-fifth of its mean value, 
which causes a change in the greatest elongation from 
16° to 29°, so that there is much more irregularity in 
this planet's motions than in the case of Venus. 

Mercury and Venus are called inferior planets, as 
their orbits are within that of the earth ; the other 
planets exhibit motions of a different character, not 
being limited to a certain distance from the sun, but, 
moving westward from him continually, they arrive at 
the opposite quarter of the heavens ; after which, still 
moving westward with respect to the sun, they begin to 
approach him on the eastern side ; so that instead of 
oscillating about the sun as the inferior planets appear 
to do, these superior planets, as they are termed, make a 
complete circuit of the heavens in an easterly direction 
with reference to the sun, the result of the sun's appar- 
ent motion eastward being more rapid than that of these 
planets, in consequence of which they lag behind him; 
though their motion among the stars is, on the whole, 
eastward like the sun's, but slower, and with periods of 
movement in the opposite direction at certain intervals. 
To fix our ideas let us take the case of the planet Mars. 
Starting from conjunction with the sun, Mars will 
appear as a morning star, rising earlier and earlier 
(by solar time) every day till he comes to opposition, 
5 



G6 MOTION AND PHASES OF MASS. 

at wliich time he passes the meridian at midnight, 
exactly opposite to the sun, and is visible all n : ght j 
continuing the same course he now rises before sunset 
and sets before sunrise, and thus becomes an evening 
star, which he continues to be until his westward 
course with respect to the sun brings him so near the 
sun's direction that he sets almost at the same time. 
and is thus lost in his rays. The period of tin bo 
changes is two years and two months nearly, during 




waich time the earth has gained one revolution on 
Mars, as he has been continually lagging behind the 
sun in his apparent yearly round, so that Mars must 
have made 1£ revolutions in 2| years, whence his y.ar 
is V of mrs, or more accurately, G87 days. All this 
time lie has presented to us a full, or nearly full, disc, 
so that we must always be looking at th • same side as 
the sun does, Hnd he can never be between us and 
the sun, as is the case with an inferior planet; whence 
it follows that Mars describes an orbit about the sun 
(which extended observations show to be somewhaft 
oval, the greatest and least distances from the sun 
being in the proportion of 9 to 11), and that this orbit 
is altogether outside that of the earth. The diameter 
of Mais is five times as great in opposition as in con- 
junction, while in the latter position he is iurther 
dislant from us than in the former by the breadth of 



MOTIONS OF THE OTHER SUPERIOR PLANETS. 67 

the earth's orbit, which is therefore, four times his dis- 
tance from us at opposition. From this it follows that 
the earth's distance from the sun is twice her 
distance from Mars when we are in a line be- 
tween him and the sun, whence the distance of 
Mars from the sun is three times his least distance 




from us, or 1-| times our distance from the sun. The 
motions of the other superior planets are generally 
similar. Jupiter's year is nearly twelve of ours, 
the intervals between successive oppositions being 
nearly a twelfth part more than a year, or thirteen 
months ; his distance from the sun is rather over 
five times that of the earth, so that his distance from 
us only varies from four to six times the earth's 
distance from the sun. The intervals between succes- 
sive oppositions for Saturn are only a fortnight over a 
year, in which time he must have described one-thir- 
tieth of his revolution, whence his year is nearly thirty of 
ours, and his path round the sun is described at a dist- 
ance 9^- times as great as that of the earth. These were 
all the planets known to the ancients, but two more 



68 THE ASTEROIDS. 

have been added since — one of which, Uranus, dis- 
covered by Sir W. Herschel in 1781, is at 19 times our 
distance from the sun, and has a year about 8-4 times 
as long as ours; the other, Neptune, was discovered 
through its attraction on Uranus; it is 30 times as far 
from the sun as we are, and its period is 164 of our 
years. 

Besides these, there is a class of bodies called Aster- 
oids, or minor planets, the first of which was discover- 
ed on the first day of this century; about 220 of 
them have been detected up to the present time, and 
every year adds some to the list. These bodies are 
as minute as they are numerous; probably none of 
them exceed 200 miles in diameter, whilst some are 
not much more than 10 miles. Their orbits all lie be- 
tween those of Mars and Jupiter, at distances ranging 
from 2h to 3^ times that of the earth, with periods of 
from 3 to 6 years. Some of their paths are very oval 
and much inclined to the earth's orbit, presenting a 
marked contrast in this respect to the large planets, 
especially the outer ones. These asteroids seem to 
form a connecting link in the gradation from the large 
and widely separated planets to the smallest meteors, 
which perhaps constitute the zodiacal light and form 
the tails of comets. The idea has been advanced 
that these small bodies, so different from the princi- 
pal planets, may perhaps be the result of an explosion, 
which has shattered a planet formerly circulating around 
the sun in an orbit between those of Mais and Ju- 
piter, and scattered the fragments in various directions. 
Though this theory would account for the peculiari- 
ties of these minute planets, the necessity for making 
any such supposition is to a great extent removed by the 
discovery of systems of much smaller bodies, the mete- 
ors, revolving round the sun; and there remains the 
great difficulty in accepting it, that the asteroids, hav- 
ing all started from the place of explosion, must, in their 
course round the sun, all return to it, so that all their 
orbits ought to have some common point of intersec- 
tion, which is not only not the case now, but as far as 



MOTION OF PLAXETS AMONG THE STABS. 69 

we can judge from theory, never could have been true 
unless the present orbits have^been disturbed by some 
unknown cause. 

Thus far we have confined our attention to the ap- 
parent motions of the planets with respect to the sun, 
so as to present the subject in its simplest form; by 
allowing for the motion of the sun among the stars 
it will not be very difficult to find that of the planets. 
The first point of which we must take account is that, 
since they move nearly uniformly in circles about the 
sun, they will appear to move faster with reference to 
the sun when they are near us. It is further neces- 
sary to distinguish between inferior and superior plan- 
ets: the former oscillate about the sun, moving some- 
times eastward sometimes westward to or from him; 
the latter move round and round always westward, as 
explained above. Taking any inferior planet at su- 
perior conjunction, the planet is moving eastward 
from the sun, and the sun is moving eastward among 
the stars, so that the planet's motion among the stars 
is eastward, or direct, as it is called; this will continue 
till the planet has turned, and its motion toward the 
sun has become cquil to the sun's motion among the 
stars, when for the moment it will be stationary among 
the stars, after which the planet's apparent motion 
toward the sun will become more rapid as it gets 
near the earth; and moving faster westward toward 
the sun than the sun does among the stars, its motion 
among the stars will also be westward or retrograde. 
This will always be the case at inferior conjunction, for 
the several planets move more quickly the nearer they 
are to the sun, the time they take to complete their cir- 
cles decreasing more rapidly than the size of those cir- 
cles as we go from the outer planets to the inner; thus 
Venus takes xVof the time taken by the earth, but her 
circle is | of that of the earth, which is a larger fraction 
than tV (f is equal to ff and T V to If)- The velocities 
of the different planets are given in the table at the 
end. 

Let us now take the case of a superior planet. In 



70 CA USE OF APPARENT RE TROGRA DE MO TION. 

conjunction its motion westward with respect to the 
sun is less than the sun's motion eastward, so that its 
resulting motion among the stars is eastward, or direct, 
just as in the case of an inferior planet. As opposition 
is approached, the motion westward with respect to 
the sun increases till it becomes equal to the sun's 
eastward motion, when the planet is for the moment 
stationary among the stars, after which, the westward 
motion still increasing, the planet will move among 
the stars in a westward or retrograde direction. 

These may be taken as the results of observation, 
but it is desirable to explain how they follow from the 
motions of the planets in their orbits with the veloc- 
ities given above. At superior conjunction, whether 
for an inferior or superior planet, the earth and the 
planet are on opposite sides of the sun, and are there- 
fore moving in opposite directions, so that the earth's 
motion makes the planet appear to move faster east- 
ward, the effect of a motion of the spectator being, 
as explained before, to make objects move in the 
opposite direction. At inferior conjunction for an in- 
ferior planet, or at opposition for a superior, the earth 
and the planet, being on the same side of the sun, are 
moving in the same direction; in the case of an infe- 
rior planet the planet's motion is greater than that of 
the earth, and is westward, as seen from the earth, 
which is outside the orbit, in the same way as sun- 
spots, as seen from the earth, move from east to west, 
though the sun's rotation is, like the motions of the 
planets, eastward. From this it results that at inferior 
conjunction the planet appears to move westward, as 
if it had a velocity equal to the difference between its 
actual velocity and that of the earth; this would be 
for Mercury about 11 miles, and for Venus about 3 
miles in a second. In the case of a superior planet in 
opposition, the earth's motion makes the planet appear 
to travel westward faster than the planet actually 
moves eastward in its orbit, so that the apparent motion 
among the stars is westward, Mars seeming to move 
with a velocity of 3^ miles in a second, Jupiter with 



ITS AMOUNT. 



71 




a velocity of 10 miles, Saturn of 12_ miles, Uranus 
of 14, and Neptune of 15, being the difference between 
the earth's velocity and that of these several planets 
in their orbits. Of course in intermediate positions 

between conjunction 
and opposition, or su- 
perior and inferior 
conjunction, we shall 
have intermediate 
motions, the appar- 
ent movement being 
M ' in every case retro- 
grade lor a greater or 
less arc about infer- 
ior conjunction or 
opposition. It may 
at first sight seem 
strange that the 
earth's motion 
should, at the same 
time make an infer- 
ior planet at inferior 
conjunction and a su- 
perior planet in opposition appear to move in oppo- 
site directions, but this is readily explained by the 
circumstance that the planets in the two cases are 
on opposite sides of us, it being understood that 
east and west merely refer to the sense in which 
a planet turns, a westward motion being in the 
same direction as the sun's daily motion, from its 
rising in the east to its setting in the west; so 
that the east and west parts of any orbit simply 
depend on the point from which we are looking 
at it, the east being to our left and the west to our 
right as we look south, and just the opposite as we 
look north. 

Since Mercury and Venus pass between the earth 
and the sun at inferior conjunction, they will sometimes 
cause partial eclipses, though from their small apparent 
size the quantity of light they cut off, when directly 



CONJUNCTION AND OPPO-ITION OP VENUS, 
THE EARTH, AND MAKS. 

The arrows show the motions of the sev- 
eral planets in equal times. 



72 TRANSITS OF MERCURY. 

between us and the sun, is scarcely appreciable, these 
planets passing over the sun's disc as small round 
black spots, on account of which these phenomena are 
not called eclipses but transits (i. e., passages). Just 
as in the case of eclipses caused by the moon, such 
transits will only occur when the planet is near one of 
its nodes ; now if Mercury be in its node at one in- 
ferior conjunction, when it next comes to inferior con- 
junction, Mercury will have made 1^ revolutions, and 
the earth a third of a revolution about, so that it will 
be far from the node of Mercury's orbit, and the 
planet therefore out of the direct line between the earth 
and the sun. Next time the earth will have moved 
through two-thirds of a revolution from the first posi- 
tion, and at the third conjunction will have returned 
nearly to the same point of its orbit, having completed 
very nearly one revolution ; if it had done so exactly 
there would be another transit, but after three inferior 
conjunctions the earth has still about 2V of a revolution 
(17^ days) to go, and is therefore too far from the 
node ; after another three conjunctions it will be A of 
a revolution short, and so on, until after 21 conjunc- 
tions it has fallen a third of a revolution behind the 
starting place, so that the next conjunction brings it 
very near the node again (within one day about), Mer- 
cury having completed 29 revolutions in 7 years, very 
nearly, and another transit may now take place. The 
return to the node would fall between the sixth and 
seventh years, so that after thirteen years there is a 
more exact return, and transits generally happen after 
this interval, though the eccentricity of Mercury's orbit 
introduces considerable irregularity into these periods. 
All this refers to one node only; at the other there will 
be another series of transits. 

In the case of Venus, whose year is ft of ours, the 
return to the node will take place very nearly alter s 
of our years or 13 of those of Venus. Venus beingthen 
only 1-^ days from node may again transit the sun, but 
after another 8 years she will be three days off, and the 
tilt of her 01 bit taking ( iTo<_ t, no transit will occur ; nor 



TEAXSITS OF VENUS. 73 

will one take place again till after 235 years, when the 
error of 1-i- days of the motion of Venus in every 8 
years has amounted to one-fifth of 225 days, so that 
another of the five conjunctions which take place in 
eight years at different parts of the orbit of Venus 
will now fall at the node. The ascending node of 
Venus is in a line with the earth at the beginning of 
December, and transits have taken place in that month 
in 1631, 1G39, and 1874, followed by one in 1882 ; at 
the descending node the transits, which occur always 
in June, are those of 1761, 1769, 2004, and 2012. 
Transits of Venus are of the greatest value to the as- 
tronomer for the means which they afford of determin- 
ing the sun's distance, and thus fixing the scale of the 
whole solar system. The distance of the sun is so 
enormous as compared with any base line we can get on 
the earth, that his parallax can not be determined with 
sufficient accuracy by the method used for the moon ; 
but as the planet Venus, when nearest, is only f of the 
sun's distance, the parallactic shift will be I, or 3^ times 
that of the sun. Even this quantity is very small, and 
instead of attempting to determine it directly it is better 
to find the shift of Venus relatively to the sun. This is 
a slightly different problem from the other, for in this 
case we only determine how much more Venus is 
shifted than the sun, and not the absolute shift of 
either. When two bodies at different distances are seen 
on the same straight line, the nearer appears to be 
shifted relatively to the other by a shift in the spec- 
tator's position, but in the opposite direction. If each 
body be removed to twice its distance from the spec- 
tator, thus keeping the distances in the same propor- 
tion, the amount of this shift will be halved, whilst if 
they be each brought to half their original distances it 
will be doubled. If then the proportion of these dis- 
tances be known, the shift or parallactic displacement 
will enable us to determine both the distances. Now, 
in the case of Venus and the sun, the proportion of 
the distances can be found with the greatest accuracy 
by means of the periods of revolutions of Venus and 



74 DETERMINATION OF SUN'S PARALLAX. 

the earth, as will be explained shortly, the approximate 
ratio found from the changes in the diameter of Venus 
being f. Thus the shift of Venus being 3^- times that 
of the sun, her shift relatively to the sun will be 2£ 
times the same quantity. The most accurate way of 
measuring the very small quantity we are dealing with 
is to refer it to the very slow motion of Venus in her 
passage across the sun's disc, by noting at two stations 
widely apart the exact instant at which that planet is 
seen to enter wholly on the sun's disc, or to begin to 
leave it. In order that parallax may produce its 
greatest effect on the time of ingress, the shift must 
be perpendicular to the sun's limb where Venus enters, 
and therefore the two stations should be separated 
from each other in the direction of a line joining this 
point with the sun's centre. 

In the transit of 1874 Venus crossed the northern 
part of the sun's face obliquely in a northwest direc- 
tion, and Australia is nearly in the middle of the 
hemisphere which was turned towards the sun at in- 
gress, whilst the Indian Ocean occupied that position 
at egress some 3^- hours later. The best stations for 
ingress were therefore in the North Pacific and in 
the Southern Ocean, about 10° due south of the ( 'ape 
of Good Hope, and for egress in Siberia and on the 
Antartic continent. * The greatest shift would be 
produced when the sun was at opposite points of the 
horizon for the two stations ; but as in that case we 
could not see the phenomenon well on account of the 
low altitude of the sun, the stations were so chosen 
that the sun was sufficiently high, and yet that the 
parallactic shift was considerable. 

In the transit of 188"-2 Venus passes, still in a north- 
west direction, over the south part of the sun's face, 

*The explanation given in the case of the moon's parallax, 
with the accompanying figure, on page .*><>, will assist the 
reader in understanding this clearly. In the lower left-hand 
figure, d will represent Venus at egress on the sun's disc re- 

irse 1. i. e., as she would be seen from the other side of the 
sun, if it were transparent and we looked through it. 



DELISLE'S METHOD. 75 

the transit occurring before she arrives at the ascend- 
ing node. At ingress the east of Brazil, and at egress 
the West Pacific Ocean, are respectively in the middle 
of the hemisphere turned towards the sun, so that in- 
gress is most retarded on the west coast of North 
America, and most accelerated at Kerguelen's Island, 
while for corresponding effects at egress Australia 
and the North Pacific are the best positions.* 

So far we have considered the effect of parallax on 
the ingress at two places, as distinct from the effect. 
on the instant of egress, which is Delisle's method of 
treating the question; and this implies that we can 
compare the clocks at the two stations so as to know 
the difference of the two observed times. Now the 
only way of doing this for places not connected by 
telegraph, is to set the clock to local time, and then 
to determine the difference between local and Wash- 
ington time, or the longitude of the place, which may 
be done by the help of the moon, as explained in 
Chapter III, and if a large number of observations 
be made, the value of the longitude so found will 
probably be true to a single second. Now the quan- 
tity we have to measure is, under the most favorable 
circumstances, only 50 seconds of arc, a magnitude 
barely visible to the naked eye, and Venus takes 25 
minutes of time to move over this space on the sun's 
disc, so that an error of one or two seconds in setting 
the clock to Washingtim time at the different stations 
is not of so much consequence. 

Another method has, however, been proposed for tak- 
ing advantage of this slow motion of the planet without 
the necessity of setting the clocks to Washington time. 
Suppose we can find a station at which ingress will be 
accelerated and egress retarded, and therefore the dura- 

*The American astronomers have pointed out three base 
lines, all centering' in ths United States, as those presenting 
the be&t positions for observing- the transit. The other ex- 
tremities of these lines lie respectively: 1, between Madagas- 
car and the Gape of Good Hope; 2, near Cape Horn; and 3, 
from New Zealand to Australia. 



76 HALLEY'S METHOD— PHOTOGRAPHY. 

tion of the whole transit lengthened, and another 
station at which exactly opposite effects will be pro- 
duced and the duration shortened, then it is evident 
that it is sufficient to observe these two durations 
without comparing the clocks, and this is the method 
which Halley proposed. This difference of duration 
is the result of two causes : In the first place, an ob- 
server at a northern station saw Venus further south, 
and therefore nearer the sun's centre, in the transit of 
1874, which lengthened the path across the sun ; and, 
in the second place, the rotation of the earth carried 
the observer further to the east at egress, and there- 
fore apparently shifted Venus to the west, and so 
hastened the egress. But this latter cause affected 
both northern and southern stations nearly alike in the 
transit of 1874, so that we have only to consider the 
difference of paths, which was greatest for stations in 
Siberia and the Antartic continent, the north and 
south parts of the hemisphere turned to the sun. In 
the transit of 1882, the longer path corresponds to the 
southern station; and further, as the south pole is 
turned toward the sun, if a station were taken near 
the south part of the earth's disc as seen from the sun, 
the earth's rotation would carry the place westward 
(the sun being below the pole), and therefore still 
further lengthen the duration of transit as compared 
with a place on the west coast of North America, 
where the earth's rotation combines with the paral- 
lactic shift to shorten the duration. But unfortunately 
some of the places which give the greatest parallactic 
shift are practically inaccessible, and astronomers have 
to be content with the best available islands in the 
southern seas, the great Antartic continent being 
virtually closed against them. 

Before dismissing this subject we must allude t<» 
another valuable method, in which photographs of the 
sun, with Venus as a black spot on his face, taken 
during transit, at northern and southern stations, have 
been made use of, the quantities compared being in this 
case the distances of the planet from the sun's centre, 



OPPOSITIONS OF MARS—VELOCITY OF LIGHT. 77 

as measured afterwards on the photographs. The way 
in which these measures may be made available will 
readily be seen by considering that a comparison of 
the times when Venus is at the same distance from the 
sun's centre for two stations is exactly equivalent to a 
comparison of the times when the planet is at the 
distance of the sun's semi-diameter, i. e., on the sun's 
limb at ingress or egress, the case which has been 
already considered. The same result may be obtained 
by measuring the distance between the centres during 
the transit ; but though such measures may be made 
with great accuracy, the photographs have the ad- 
vantage of giving a permanent record, which can be 
examined with the greatest care afterwards. 

Though transits of Venus offer the most favorable 
opportunity of determining the sun's distance, they are 
such rare phenomena that astronomers have not been 
content with trusting to them alone, but have ob- 
tained very accurate results from another planet, 
Mars, which, in opposition, approaches us almost as 
closely as Venus herself ; this is especially the case 
when the opposition of Mars takes place in that part 
of his oval where he is nearest to the sun, which will 
bring him nearer to us by a fifth part of his average 
distance in opposition, whilst, if this take place in 
summer, when the earth is farthest from the sun, the 
distance between the two bodies will be still smaller, 
being less than I of the sun's distance. The mode of 
observation is exactly the same as in the case of the 
moon, though the quantity to be measured is a 
hundred times smaller, so that there must necessarily 
be considerable uncertainty ; it appears, however, 
from the comparison of many observations made in 
the northern and southern hemispheres, in the favor- 
able oppositions of 1862 and 1877, that Encke's value 
of the sun's parallax, deduced from observations of 
the transit of Venus in 1769, was some tv of 
a second of arc in error, and that the sun's distance 
was in consequence over-estimated, making it 
about 93 millions of miles instead of 95 millions, 



78 ECLIPSES OF JUPITER'S MOONS. 

an error which has been referred to a misunderstand- 
ing about the place of the transit seen by some of the 
observers. This correction is supported by an indirect 
determination of the sun's distance, from the velocity 
of light and the time it takes to reach us from the sun, 
in consequence of which eclipses of Jupiter's moons 
(of which there are four) are found to take place, on 
the average, 8^ minutes earlier than the predicted 
times when we ave nearest to him in opposition, and 
8^ minutes later when we are on the opposite side and 
Jupiter near conjunction, light having then to traverse 
the extra distance across the earth's orbit as compared 
with the length of its journey in the former case, from 
which it is inferred that light takes 16£ minutes to 
traverse the earth's orbit, which, with a velocity of 
about 186,000 miles a second, makes the distance of 
the sun 93 millions of miles. Nearly the same result 
follows from the relation between the velocity of the 
earth in her orbit and the velocity of light. If the 
earth were at rest we should see all the heavenly 
bodies in their actual places, but as the earth is mov- 
ing with about a ten-thousandth part of the velocity 
of light, the light of a star will seem to come from a 
slightly different direction in consequence of our own 
motion. This effect was first observed by Bradley, 
and the true explanation of this apparent deviation in 
the position of a star (which he called aberration) was 
suggested to him by observing that when a boat was 
beating up against a head-wind, the vane pointed in 
slightly different directions according as the boat was 
moving in one direction or the other. Thus with a 
side-wind the boat's motion would make the wind Beem 
a little ahead, as by its passage through the air the 
boat would make a slight head-wind, which, combining 
with the real breeze, would make it seem to blow a 
little from the bow of the boat, whichever way that 
might be. Thus, suppose the wind blowing from the 
north, if the boat be sailing in an easterly direction 
the wind will, according to the vane, seem to come a 
little from the east, say N.N.E., while it will apparently 



DIRECT PROOF OF EARTH'S MOTION. 79. 

shift to N.N.W. when the boat sails in a westerly 
direction. The same effect may be noticed from the 
motion of a carriage, or when running with a side- 
wind, the result being that the wind seems to come 
more from the direction in which we are moving. 
Just the same happens with the light of a star, which, 
like the wind, appears to come rather more in the 
direction in which the earth is moving. It is accord- 
ingly found that the apparent position of a star shifts 
with the direction of the earth's motion, the shift be- 
ing greatest when the earth is moving sideways with 
respect to the star's direction, and nothing at all when 
directly to or. from it. The faster the earth moves the 
greater will be this apparent shift, and the proportion 
of the earth's velocity to that of light will be given by 
the amount of shift. It may be remarked that the 
aberration of stars affords us a direct proof of the 
motion of the earth round the sun, as such a shift can 
not be accounted for on any other supposition. In 
the case of the planets there will be a double shift, 
caused by the planets' and the earth's motions together; 
and instead of allowing for both of these separately, 
it is more convenient to find, from the known distance 
of the planet at the instant, the time which light takes 
to reach us from it, and to consider that the observa- 
tion was made so much earlier, or, in other words, to 
antedate the observation by this interval. A little 
consideration will show that this amounts to the same 
thing as correcting for the shift; for the earth's motion 
will shift the planet apparently forward (**. e., in the 
direction of this motion) by the space through which 
the earth has moved while the ray was coming, and 
thus the planet will be seen in the same direction 
as if it remained where it was when the ray left it 
and the earth was shifted back to its position at 
the same instant, since, as we have already explained, 
such a shift of the earth backward will apparently 
shift the planet forward through the same space. 
Tables being formed which give the places of the 
planets and the earth at any instant, it is thus easy to 



80 KEPLER'S THIRD LAW. 

compare the observations made at any particular time 
with the places from the tables for an instant preced- 
ing this by the number of seconds which light takes to 
cover the distance between the planet and us, and thus 
the accuracy of the tables can be checked and correc- 
tions to them made when necessary. 

On comparing the velocities of different planets 
with their distances from the sun it will be seen that 
the former decrease as the distances increase, but not 
so rapidly; thus the velocity* of Mars is half that of 
Mercury, but his distance is lour times as great; the ve- 
locity of Saturn is one-third that of the earth, but his 
distance is about nine times as great; the velocity of 
Uranus is about one-fifth that of Venus, whilst his dis- 
tance is nearly twenty-five times as great. Now these 
numbers (which are only approximate) suggest a con- 
nection between the velocity of a planet in its orbit 
and its distance from the sun, of such a kind that the 
distance increases as the square of the velocity de- 
creases; thus the square of the velocity of Mars is one- 
fourth that of Mercury, while the distance is four times, 
and where more exact calculations are made this rule 
is found to hold in all cases. This great law was dis- 
covered by Kepler, and was put by him in a slightly 
different form, viz.: that the squares of the periodic 
times, or years, of the several planets incre ise as the 
cubes of their distances from the sun. This follows 
from what has just been stated, since tip- p sriod in- 
creases as the size of the circle increases and as the 
velocity decreases; so that the square of the periodic 
time increases as the square of the distance from the 
sun increases, and as the square of the velocity de- 
creases. But the square of the velocity decreases as 
the distance increases, whence finally the Bquare of the 
periodic time increases as the cube of the distance. 
This is known as Kepler's Third Law, the other two. 
which were derived from laborious calculations found- 
ed on a large number of observations of the planet 
Mars in the first instance, and afterwards extended to 
the other planets, are: first, The planets describe el- 



KEPLER'S EIEST AXD SECOXD LAWS. 



81 



lipses* (or ovals), of which the sun occupies one focus; 
second, the motion in these curves is more rapid in 
the part of the curve nearest the sun, so that the fan- 
shaped sector which the line drawn from the sun to 
the planet sweeps out in one day ( or in one month ) 
will be of the same area, though of a different shape, 
in all parts of the orbit, the angle being larger when 
the distance from the sun is less. If the oval orbit be 
cut out of cardboard and cut through the points where 
the planet is at the beginning of each month, so as to 
form wedges having their points at the place of the sun, 
all these wedges will be of exactly the sain^ weight. 




MOTION IN AN ELLIPSE. 

The arcs marked off are each descri? ed in a month or twelfth 
part of the planet's year. The lines from the arrows to the 
curve show the space through which the sun draws the planet, 
in a month and in half a month respectively. The ellipse is 
rather more oval than that of the minor planet Polyhymnia, 
and twice as oval as that of Mercury. 

* An ellipse is an oval curve, which may be traced by tying 
two ends of a piece of thread to two pms fixed on a drawing 
board, so that the thread is more or less slack, and running- a 
pencil round in the slack of the thread. The two pins will be 
at the two foci, and according as the thread is more or less 
slack, i. e., the pins proportionately nearer or further apart, the 
ellipse will be less or more oval. 



82 LAW OF GRAVITATION. 

These three laws were established by Kepler as a 
result of observation; it remained for Newton to dis- 
cover the principle from which these motions follow- 
ed, in the law of universal gravitation, by virtue of 
which every particle in the universe pulls every other 
particle towards it with a fores that decreases as the 
square of the distance between the particles increases. 
Newton proved by pure reasoning that such a force 
would be capable" of making the planets move about 
the sun in accordance with Kepler's Laws, if the sun 
were supposed to consist of an enormous quantity of 
matter (in correspondence with his vast size) which 
would pull the planets, without their pull on him hav- 
ing much effect in moving his large mass. Similarly, 
the attraction between the earth and the moon would be 
capable of making the moon move in such an orbit 
as she actually describes. The next step was to show 
that the attraction of the earth, which makes an apple 
fall, is really the force that keeps the moon in her act- 
ual orbit. Now an apple (or a stone) at the earth's sur- 
face falls sixteen feet in the first second through the 
earth's attraction, and at the distance of the moon, 
which is sixty times as far from the earth's centre, it 
would fall dnJir of a foot, or about 2 \ inch in the first 
second if the force decreases as the square of the dis- 
tance increases. Now the moon really falls towards 
the earth by almost precisely this amount, thougli not 
in a direct line, for if left to herself at any instant she 
would go off in a straight line; but the earth gives 
her a pull which brings her into a curve, and the dis- 
tance between her position in this curve and the stra : ght 
line in which she would have pone off one second !»«•- 
fore, represents her fall towards the earth in the first 
secon 1, which is found to be about t l inch. It may 
appear difficult to understand how the moon can be 
continually falling towards the earth without ever reach 
ing it, but it must be remembered that her motion, 
if left free at any instant, continually tends to carry 
her away, and that it requires a continual fall towards 
the earth to keep her in her course, this fall being, of 



ILL US TEA TIONS. 83 

course, in different directions at different parts of her 
orbit, since it is always directed towards the earth. 
This continual fall * towards the centre of motion is 
made sensible in a railway car running along a sharp 
curve; the passengers seem to be thrown outwards, be- 
cause their tendency is to move in a straight line whilst 
the car is kept to the rails and being continually pull- 
ed towards the centre of the curve. In the same way 
if a stone tied to a string be whirled rapidly round, a 
strong pull on the hand holding it will be felt, and as 
soon as the string is let go the stone will fly off in the 
direction in which it was going at that instant. Al- 
though it is convenient to speak of the earth's attrac- 
tion on the moon, or the sun's on the planets, yet really 
the earth does not pull the moon more than the moon 
pulls the earth, the law of gravitation being merely 
that there is a pull between them which tends to bring 
them closer together, but the earth, being more mas- 
sive than the moon, will not be moved so much. The 
case of a large and small stone tied together by a 
string and flung into the air will illustrate this; the 
pull on each, communicated through the string, is the 
same, but the small stone will circle round the large 
one, which pursues nearly the same course as if alone, 
being pcarcely disturbed by the pull through the string. 
With the earth and moon the real state of the case is 
that every particle of the moon pulls every particle of 
the earth, and every particle of the earth pulls every 
particle of the moon with equal force; but there being 
more particles in the earth, the pull of the earth 
on any one particle of the moon is stronger than the 
pull of the moon on any one particle of the earth, 
though the pull of the earth on the moon, as a whole 
(i. e., on all its particles), is exactly equal to the 
pull of the moon on the earth as a whole. In 
consequence of this mutual pull both the earth and 

* This word is here used in an extended sense to express the 
result of a pull towards any centre, not merely to the earth's 
centre. 



84 CENTER OF GRAVITY— TIDES. 

moon will move about a point in the line joining them, 
which is much nearer the earth than the moon. This 
point is commonly called the centre of gravity of the 
two bodies, and is such that if we imagined them con- 
nected by an enormous rod, they would balance about 
this point, just as a large and small stone fixed at the 
two ends of a stick will balance about a point of the 
stick nearer the large stone. The motion of the earth 
and moon will then be exactly the same as if they were 
connected by an elastic string, a certain point of which 
(the centre of gravity of the two bodies) is made to re- 
volve round the sun once a year, whilst both earth and 
moon whirl round this point in ellipses once in a lu- 
nar month, the string stretching more or less, so that 
the distance between them alters. The motion of the 
moon as seen from the earth will then be exactly the 
same as if she were moving in an ellipse about the 
earth at rest; but the earth's motion about the sun will 
not be an exact ellipse, but an orbit, something like 
that of the moon round the sun, though the deviation 
from the true ellipse (caused by the pull of the moon) 
is very much less. 

One consequence of this pull on the earth remains 
to be noticed, viz., the tides. These are caused by the 
attraction of the moon and sun pulling the waters of 
the ocean, which are turned toward them (and there- 
fore somewhat nearer) more than the solid mass of the 
earth (which is pulled just as if it were all collected at 
the centre), and thus the water on the part turned to- 
wards the moon is heaped up: and similarly for the 
sun's action. Again, the moon (or sun) pulls the earth 
more than the water on the other side, and therefore 
draws the earth away, causing high water also on this 
side. From this it follows that there should be a lu- 
nar tide with high water when the moon is on the me- 
ridian (both above and below the horizon), and also a 
solar tide with high water at noon and midnight. And 
this tide will be higher the nearer the sun (or moon) is 
to the zenith or nadir of the place, whence it follows 
that in summer the higher of the two solar tides is at 



SPUING AND NEAP TIDES. 85 

noon, when the sun is nearer to the zenith than it is 
to the nadir at midnight, whilst in winter the oppo- 
site is the case; and similarly for the moon, according 
as she is north or south of the equator. In all this the 
earth's rotation has been neglected, the effect of this 
being to make the time of high water somewhat later, 
as the moon has passed the meridian before its attrac- 
tion has had time to produce its effect; and further, 
the reasoning only applies to the open ocean, there 
being no sensible tide in lakes and inland seas, where 
no great mass of water is acted on: even in the Medi- 
terranean the rise of the tide is hardly perceptible. 
In channels and narrow seas the tidal wave comes from 
the ocean, and often takes many hours to traverse them; 
this will make high water so much later, giving rise 
to what is known as the establishment of the port, 
or the time that high water is after the meridian pas- 
sage of the moon and sun, when they transit together 
at new and full moon. Since both sun and moon pro- 
duce tides, they will, when pulling in the same or op- 
posite directions, cause a much higher tide than when 
pulling at right angles, the high water caused by the 
sun in the latter case partly filling up the low water 
due to the moon, whibt at new or full moon the times 
of high water from both sources are the same, and they 
conspire to produce high tides, known as spring tides; 
those at first and last quarter being called neap. The 
time of high water in the open ocean is in the latter 
case intermediate between the meridian passages of 
the sun and moon. 

The height of spring tide at any place is found to 
be about 2^- times that of neap at the same place; and 
as the solar tide is added to the lunar in the former 
case and subtracted from it in the latter, it follows 
that the effects of the moon and sun are as 5 to 2. 
Now the effect of the moon in raising a tide 
(being the difference of her pull on the water 
and on the earth's centre) is the mass of the 
moon multiplied by the difference between ^r squared 
and ^V squared, which is very nearly twice the mass of 



86 RELATIVE MASS AND DENSITY OF 

the moon divided by the cube of 60.* Similarly the 
effect of the sun will be twice his mass divided by the 
cube of his distance (expressed in radii of the earth, 
as in the case of the moon), which is 23,400, and this 
latter effect is f of that of the moon, so that his mass 
is about f of 23,400 cubed divided by 60 cubed, or 
nearly f of 400 cubed, i. e., 25 million times that of 
the moon. Now the sun's diameter is 109 times that 
of the earth, whilst the earth's is not quite four times 
that, of the moon, so that the sun's diameter is about 
400 times that of the moon, and his bulk 400 cubed 
(or 64 million) times the moon's, the bulk of a globe 
being proportioned to the cube of its diameter. From 
this it follows that, as the sun's mass is f of 400 cubed 
times the moon's, his density is f of hers, the densities 
being proportional to the quantities of matter in equal 
bulk. This is only a rough approximation to the truth; 
indeed the method is not susceptible of any great ac- 
curacy, and is only given as an instance of the way 
in which one heavenly body may be weighed, as it were, 
against another. In the case of the earth and the 
sun, Kepler's Third Law enables us to find the pro- 
portion of the masses pretty accurately; for it is easy 
by this law to find the velocity with which a body 
would go round the sun at the same distance as the 
moon from the earth, though this U a purely ideal case, 
since the sun's diameter is much greater than that of 
the moon's orbit. The earth's distance from the sun 
is nearly 400 times that of the moon from the earth, 
whence the square of the velocity of this imaginary 
body going round the sun would be 400 times th- 
square of the earth's velocity in her orbit ; and as 400 
is the square of 20, we have the velocity of the ficti- 
tious body equal to 20 times the earth's velocity, or 364 
miles a second; whilst the moon's velocity under the 
influence of the earth's attraction is a little over A of 
a mile in a second. Thus the sun's attraction can re- 

* n 1 119 , • , • ,120 2 

A-*— »& Which 1S VJry nearly <WX60»-60i 



SUN AND MOON. 87 

tain a body in an orbit of the same size as the moon's 
when moving with a velocity nearly 600 times as great 
as hers, so that as the earth pulls the moon towards 
it through -3-V inch in one second, the sun would pull a 
body at the same distance through this space in ¥ fo 
of a second. Now from the laws of falling bodies, a 
body pulled through aV inch in 6<hr second would be 
pulled through 360,000 twentieths of an inch in one 
second;* so that the sun's pull in one second would 
be 360,000 times that of the earth on a body at the 
same distance, and therefore he must have 360,000 
times the number of attracting particles that the earth 
has. His mass is really about 330,000 times that of 
the earth; but his bulk is 109 cubed, or about 1,300,000 
times that of the earth, so that his density is only a 
quarter that of the earth, or about 1^- that of water, 
the density of the earth, as we shall presently see, be- 
ing about 5-g- times that of water. The moon's density 
is nearly 2-| times that of the sun, and therefore nearly 
f that of the earth, and her mass about sV of the earth's 
mass. The above method may be applied to find the 
proportion of the mass of any planet which has a 
moon, to the sun, all that is wanted being the dis- 
tance of its moon and the length of the lunation; 
but in the case of other planets the problem is more 
difficult, though astronomers are able to make a fair 
approximation to the masses of such planets by the 
help of the attraction which they exert on their neigh- 
bors, pulling them a little out of the coarse which 
they would pursue if the sun were the only attracting 
body, as he is by far the most important. The devia- 
tions from exact ellipses round the sun are, however, 

* A heavy body on the earth falls through about 16 feet in 
the first second of its fall ; 64 = 4 X 16 feet in two seconds 
from the start ; 144 = 9 X 16 feet in three seconds ; its speed 
increasing as the number of seconds from the start, and the 
space through which it is pulled by gravity as the square of the 
number of seconds. The sam3 will apply to fractions of a sec- 
ond, the space through which a body falls in T V of a second be- 
ing iio X 16 = 0.16 foot; in gjo °f a second ffg -J§-jnj- foot. 



88 MASS AND DENSITY OF THE EARTH. 

so small that it is only whore great accuracy is aimed 
at that the application of Kepler's Laws has to be 
slightly modified; the only exception being the moon, 
which is greatly disturbed by the sun's attraction. 

It remains now to determine the mass of the earth 
as compared with our unit of mass, as a pound (or a 
kilogramme). Three methods have been used for 
solving this problem. The first compares the attrac- 
tion of a mountain with that of the earth by observing 
the deflection of a plumb line on opposite sides of the 
mountain, the angle between the zenith (which is the 
direction of the plumb line) and the poie being hums 
ured, and allowance made for the distance in miles 
that one station is north of the other. Now the mass 
of the mountain in tons can be found from its size and 
average density, and its average distance from 
station being known, as well as that of the earth's 
centre, the comparison of the attractions of the earth 
and mountain gives the mass of the earth in terms of 
that of the mountain, and therefore ultimately in tons. 
In this way Maskelyne found that the attraction of 
the Scotch mountain Schehallien was about ^offffth part 
of that of the earth, and the same method has been 
applied to other mountains. The second method is 
known as the Cavendish experiment. In this case 
the deflection of two balls connected by a light wood- 
en rod, and suspended in a horizontal position by a 
long wire attached to the middle of the rod, was ob- 
served when two large leaden balls of known mass 
were brought near the suspended balls. The attrac- 
tion of the earth on the latter could be inferred from 
the time in which they vibrated horizontally (by the 
twisting and untwisting of the wire), and the propor- 
tion of the earth's attraction to that of the leaden balls 
was thus obtained, and from this the mass of the 
earth. The principle of the third method, which was 
applied by Sir George Airy in the Harton pit. is to 
find the difference between the attraction of the earth 
at the surface and at the bottom of a coal mine, where 
the attraction of all the outer layer produces no effect 



BODE'S LAW. 89 

In this case the attractions were measured by observ- 
ing- the number of vibrations made in equal times by 
a pendulum at the surface and at the bottom of the 
mine, the force which makes the pendulum oscillate 
varying as the square of the number of vibrations in 
a given time. A pendulum at the bottom of the mine 
was found to gain 2^ seconds a day more than at the 
surface, and the density of the earth was hence con- 
cluded to be about 6|- times that of water. The other 
methods gave smaller values, so that the average of 
all the determinations gives a density of about 5^- 
times that of water, or twice that of surface strata. 
The bulk of the earth being known in cubic miles 
from its radius, there is no difficulty in calculating 
its mass in tons; but the number is so enormous, that 
it conveys no idea to the mind, and is therefore not 
given hire. 

A curious progression has been observed to hold 
approximately in the distances of the planets from the 
sun; and, though no reason' has been given for any 
such law, it is a useful aid to the memory, and de- 
serves mention from its having called attention to the 
gap between Mars and Jupiter, and thus led to the 
discovery of the minor planets. According to this 
so-called law of Bode (or Titius), the intervals between 
the orbit of Mercury and those of the other planets go 
on doubling as we proceed outwards, the distance 
from the sun of the several planets, Mercury, Venus, 
the Earth, &c, being roughly as the numbers, 4, 7, 10, 
16, 28, 52, &c., or, 4; 4+3; 4+3x2; 4-f 3x4; 4+3x8; 
4+3x16, &c. ; but it must be remarked that the dis- 
tance of Neptune, according to this law, should be 392 
instead of 300, its real value. 

Thus far the size and density of the planets have been 
considered, but when they are examined with a power- 
ful telescope some further information may be gained, 
the chief point being the determination of the period 
of rotation, which is found, as in the case of the Sun, 
by watching the movement of any markings which 
may be seen on the disc. Li this respect the planets, 



90 ROTATION OF PLANETS. 

which all, as far as is known, turn from west to east, 
like the sun and the earth, may be divided into two 
classes, the four inner, Mercury, Venus, the Earth, and 
Mars, rotating in about the same time, whilst the day 
for Jupiter and Saturn (and perhaps for Uranus and 
Neptune) is about ten hours. In the case of Mercury 




COMPARATIVE STZES OF THE PLANET8. 

and Venus, evidence as to markings or spots is so con- 
flicting that very little confidence can be placed in the 
values°given for the length of their day. They an- 
generally seen as brilliant spotless discs, gibbous of 
horned, like the moon ; Venus in particular being so 



ASPECT OF MERCURY— VENUS— MASS. 91 

dazzlingly white in a powerful telescope as to require 
the use of a colored glass to moderate her light. 
Mercury is about three-eighths of the size* of the 
earth, whilst Venus is nearly as large as the earth, and 
of about the same density. Next to nothing is known 
of their physical nature, except that they show in their 
transits across the sun signs of an extensive atmos- 
phere, giving rise to a ring of lig-ht, which is seen 
round the edge outside the sun's disc, and probably 
the cloudy state of this atmosphere prevents our ever 
seeing the real body of either. 

The case is very different with Mars, which exhibits 
well-defined ruddy and blue-grey markings, which have 
been called respectively continents and seas, besides 
white spots at the poles of rotation, — supposed to be 
snow or ice. These conclusions can only be accepted 
provisionally, but there is, at any rate, more justifica- 
tion for the terms than in the case of the moon ; Mars 
having probably an extensive atmosphere. He is 
rather more than half the size of the earth, and of 
somewhat less than f of its density. 

Of such minute bodies as the asteroids nothing is to 
be made out ; but the next planet, Jupiter, is a magni- 
ficent spectacle, being more than ten times the size of 
the earth, though only ^ of its density, and attended 
by four moons about the size of ours. These some- 
times cross his disc, the shadow being also seen to tra- 
verse it, thus causing an eclipse of the sun to the in- 
habitants of Jupiter ; whilst at other times they are 
themselves eclipsed in the planet's shadow, or occulted 
behind his disc. These two latter phenomena are quite 
distinct, the former taking place when the satellite is 
hidden from the sun, though to us, perhaps, apparently 
at some distance from the planet's disc, the latter when 
the satellite is hidden from us. The times at which 
these two phenomena occur will be different unless 
the earth and sun happen to be in a line with the 
planet, which will be the case in opposition. Before 

*This word is used as referring to diameter, not bulk. 



92 JUPITER. 

opposition, Jupiter being eastward of the prolongation 
of the line joining the earth and sun, the eclipses will 
take place when the satellites are west of the planet, 
the earth looking round that side as it were, whilst 
after opposition the reverse will be the case. The 
motions of the satellites are eastward, and, like our 
moon, they have been supposed to turn on their axes 
once in each revolution round the planet, certain vari- 
ations of brightness having been observed to recur at 
such intervals, as if a dark and a bright side were turned 
towards us in succession. Their orbits are very 
slightly inclined to that of Jupiter, so that eclipses of 
the three inner moons occur every lunation, and of the 
fourth less frequently, Jupiter's shadow being large as 
compared with their distances. Their periods are If, 
3^, 7£, and 16f days, respectively, and their distances 
G, 9f, 15^, and 27 times the radius of the planet. 

The disc of Jupiter is usually distinguished bv 
several bright belts, parallel (or nearly so) to his equa- 
tor. These have been supposed to be clouds formed 
by the trade winds, which, from his rapid rotation, 
must be nearly due east, and the rapid changes in the 
form of the belts confirm this idea. Some of the 
belts are reddish, with dark belts between of greenish 
grey, and this variety of hue seems more marked in 
some years than in others. 

Somewhat similar belts are seen on Saturn, but the 
striking feature of that planet is a wonderful ring, 
or rather system of rings, nearly 140,000 miles id 
diameter (or one-third the size of the moon's orbit), 
which we see more or less edgeways, they being in- 
clined some 28° to Saturn's path. When we are 
nearly in a line with the crossing points (or nodes) of 
the ring with our plane, they are seen as a bright fine 
line crossing the planet parallel to the belts; this line 
disappears altogether when we see the rings exactly 
edgeways, so that the thickness must be very small, 
perhaps not more than a hundred miles. These 
disappearances will occur at intervals of nearly 
fifteen yeaA, half the Saturnian year, there being 



SATURN. 



93 



two parts of this orbit corresponding to our spring 
and autumn, for which the ring is placed edgeways 
with respect to the sun, and therefore nearly so to 
the earth, which to an inhabitant of Saturn never 
seems to wander more than 6° on either side of the Sun. 
When the earth and Sun look at opposite sides of the 
ring (which is sometimes the case about the time of 

1869 1872 




phases of satuen's rings from 1869 to 1877, and from 
1878 to 1885. (For the latter turn the figures iqjside clown.) 

The figures are not intended to show the tilt with reference to 
the ecliptic, which can be inferred from the figure of the 
• Seasons, p. 37. 



94 PHASES OF SATURN'S RINGS. 

disappearance) it will only be seen as a black belt 
crossing the planet, and invisible outside the disc; 
in such cases there will be two disappearances close 
together, the first when the earth crosses from the 
bnght side to the dark, and the second when it returns 
from the dark to the bright side of the ring. 1 he 
phases presented by Saturn's ring are exactly analo- 
gous to the appearances of the earth's equator to a spec- 
tator on the Sun, which we have already described 
with reference to the seasons, remembering that the 
vear for Saturn is nearly thirty of our years, and that 
we do not always see the rings exactly as they would 
be seen from the sun. 

Thus, starting from what would be spring for Saturn s 
northern hemisphere, when the ring is seen edgeways, 
the northern side will be presented more and more 
fully to us, till, after 71 years, we get to Saturn s 
northern summer ; the rings will after this appear to 
close up, disappearing at Saturn's autumnal equinox 
after 7-J- years more, from which point the Southern 
side is seen for fifteen years, going through the same 
phases as the northern. 

The svstem of rings consists of three bright and an 
interior" dusky ring, which seems to be semi-trans- 
parent, allowing the body of the planet to be seen 
through it. How such a system can be preserved 
against the slightest disturbance from the attraction 
of other bodies has puzzled mathematicians, and after 
making various hypotheses they have been forced to 
the conclusion that the rings, if solid, liquid, or even 
o-aseous, must inevitably end in being precipitated on 
to the planet unbroken, the only available alternative 
being that each ring, instead of being a coherent mass, 
consists of a large number of minute bodies revolving 
round Saturn like satellites, and forming an appen- 
dage somewhat similar to the zodiacal light round the 
sun. Saturn is nearly ten times the diameter of the 
earth, but only on the whole one-ninth as dense, or 
two thirds the density of water, but how much of his 
bulk is composed of atmosphsre we have little means 



URANUS AND NEPTUNE. 95 

of judging, and can therefore say nothing of the 
density of the true body of the planet (if he have 
any), "though we know that his mass is nearly 100 
times that of the earth, his bulk, including his atmos- 
phere, being nearly 1,000 times the earth's. A similar 
remark applies to Jupiter, which has also in all prob- 
ability, a very extensive atmosphere. Saturn is at- 
tended by eight moons, revolving in periods ranging 
from 1 to 80 days, and at distances of from 3J to 64 
times the radius of the planet, or from a half to ten 
times the distance of our moon. 

Uranus and Neptune are so far off that very little 
can be made out about them, except that they have 
nearly circular discs of 4" and o" apparent diameter 
respectively, corresponding to a real diameter of 4|- 
and ok times that of the earth, whilst the density of 
Uranus is a fifth, and that of Neptune, a seventh of 
the earth's, or not far from the density of water. Four 
satellites to Uranus and one to Neptune have been 
discovered up to the present time, but there are only 
a very few telescopes in the world capable of showing 
them, so faint is their light. In the case of Uranus, 
the moons move in paths very much inclined to that 
of the planet round the sun, and in a retrograde or 
westward direction. 

The conditions to which the several planets are ex- 
posed are so various that it is difficult to form any 
conception of their state ; to Mercury the sun appears 
seven times as large in area as to the earth, whilst to 
Neptune he appears of only -r^th the area, and the 
amount of light and heat received by these bodies 
will be proportional to the apparent area of the sun's 
disc, and therefore to these numbers. What pro- 
portion of this heat is reflected away into space by 
the atmospheres of the several planets is not exactly 
known, nor the effect that clouds may have in pre- 
venting the radiation of heat which takes place 
with a clear sky : but it is difficult to see how 
causes of this kind could operate to such an 
extent as to raise the surfaces of the outer planets, 



96 PHYSICAL CONDITIONS FOR THE PI ANETS. 

Uranus and Neptune, much above the temperature of 
space, which is known to be much farther below the 
freezing point than that is below the boiling point of 
water; though internal heat may in these bodies be far 
greater than that of the earth, and thus keep up a 
comparatively high temperature without much help 
from the sun. 

Further, the force which makes bodies fall must be 
very different for the several planets. On the sun it 
would be twenty-seven times that on the earth, on 
Jupiter two-and-a-half times, on Saturn and Venus 
about equal to gravity on the earth, on Mars and Mer- 
cury one-half, and on the moon only one-sixth, whilst 
on the asteroids it would perhaps range from fa to 
rau. The weight of the same body being so different at 
the surfaces of different planets, volcanic and other 
forces of expansion would produce very different effects; 
and the same remark applies to muscular force. A 
man who can jump 5 feet high on the earth would be 
able to jump 30 feet on the moon, and some 2,500 feet 
on the smallest asteroid, whilst on Jupiter he could 
only jump 2 feet, and on the sun only about 2 inches; 
and the muscular effort required to raise a mass of 100 
pounds on the earth would raise 600 p minis on the 
moon, but only 4 pounds on the sun. Further, the 
rapidity of rotation, which tends to throw bodies off 
at the equator, varies greatly for the different planets, 
being very large in the case of Jupiter and Saturn, 
which causes a bulging out of their equator to the 
extent of fa and fa of their diameters respectively, 
that of the earth being only s hv, and of Mars fa. 



CHAPTER V. 



The bodies which we have next to consider, though 
belonging, at least temporarily, to the solar system, 
present peculiarities which separate them completely 



COMETS— THEIR MOTIONS. 97 

from all the planets, whether large or small. Whilst 
the planets are massive globes with definite bound- 
aries, comets are diffused bodies with no distinct out- 
line, and generally of enormous volume, hut of such 
small mass that no appreciable disturbance is caused 
in a planet's motion even by the near approach of one 
of these strange bodies. But it is not only in their 
constitution that comets differ from planets; they are 
equally remarkable for the irregularity of their 
motions. Thus in a single day the comet of 1472 
moved in the heavens through 40° (a ninth of a com- 
plete circle), and that of 1861 through 12°, the appar- 
ent motion afterwards slackening till it became hardly 
sensible, and other comets have moved nearly as rap- 
idly for a time. A considerable part of this large ap- 
parent motion arises from our own motion in the 
opposite direction to that of the comet, which in the 
cases referred to was very near the earth at the time, 
and this parallactic effect must, as in the case of the 
planets, be allowed for before we can find the true 
path of the comet about the sun. 

We saw that all the planets moved in one direction in 
nearly circular orbits,very slightly inclined to the earth's 
path (except in the case of some of the minor planets), 
but comets are found in all parts of the heavens, and 
moving in all directions, the ellipses which they describe 
being commonly much inclined to the earth's path, and 
so much elongated that in most cases they cannot be dis- 
tinguished in the portion near the sun (which is the 
only part where we can follow them) from another 
curve called a parabola, which is something like the 
half of a long ellipse, the distinction being that in the 
parabola the two branches separate further and fur- 
ther, and never come round, as is the case with the 
ellipse. The motion in these parabolas is, however, 
strictly regulated by Kepler's Second Law, that the 
sectors (or wedges) formed by lines drawn to the sun 
from the comet every day are equal in area, so that 
the motion in the part near the sun is exceedingly 
rapid, to make up for the shortness in the radii of the 
7. 



98 PARABOLA AND ELLIPSE. 

sector. Thus, Newton's comet of J 680, which passed 
within a third of the sun's radius from his surface, had 
a velocity of 250 miles a second when nearest to him, 
whilst that of 1843, which passed even closer, almost 
touching the surface, had the still greater velocity of 
370 miles a second, taking only two hours to go half 




ORBITS OF COMKTS. 



Biela's and Turtle's comets are taken as types of the Jupiter 
and Saturn class of comets respectively, and the orbits are 
made slightly less oval than the actual paths, to show how an 
ellipse may touch the earth's path on the outside, and Jupiter - 
or Saturn's path on the inside. 

round the sun. On the other hand, the comet of Faye, 
which revolves round the sun in 7 years and 5 months, 
resembles the planets most in its motions and in its 
orbit, though its least distance from the sun is only 
^ of its greatest, whilst for Mercury it is I, and lor 
one of the small planets, Polyhymnia, it is £, this 
being, perhaps, the most oval orbit among the planets. 



ORBITS OF COMETS. 99 

With regard to the inclinations of their orbits, comots 
seem rather to avoid the ecliptic, only \ of the whole 
number having inclinations lying between 0° and 30°, 
whilst about f lie between 30° and 60°, and an equal 
proportion between 60° and 90° ; and further, the 
motion in these orbits is about as often retrograde as 
direct, though the great majority of the periodic comets 
circulate in the same direction as the planets, while of 
those which move in parabolas (or exceedingly long 
ellipses), two-thirds have a retrograde or westward 
motion. The orbits of the periodic comets are also 
generally not much inclined to the paths of the earth 
and other planets. 

Comets are as various in their aspects as in their 
movements, but there is a family likeness binding 
them all together, and indicating that they are all sub- 
ject to somewhat similar conditions, A large propor- 
tion are exceedingly faint objects, only to be seen in 
large telescopes as small spots of hazy light, very few 
being visible to the naked eye, though four or five 
new comets are on the average picked up every year. 
In old times comets generally burst unexpectedly on 
the view, but this is hardly ever the case now, as 
astronomers are continually on the watch to detect any 
comet as soon as it can be seen in a powerful telescope, 
so that by the time it has become at all conspicuous its 
path is well determined, and the brightness it will 
attain is tolerably well ascertained. Since the invention 
of the telescope, astronomers have been able to watch 
the growth of large comets from their first appearance, 
as spots of nebulous light, and have thus formed some 
idea of the development of the different parts of which 
a comet consists viz., the nucleus, the coma or head, 
and the tail. Taking the case of a large comet before 
its approach to the sun, nothing will probably be seen 
but the head — a mass of hazy light, with a bright point 
in the centre called the nucleus, which is often absent 
in the small comets. As the comet comes more under 
the sun's influence near perihelion, the nucleus com- 
monly throws out jets of light towards the sun, which 



100 



GROWTH OF COMETS— THEIR TAILS. 



curve back and apparently give rise to the tail— a band 
of light sometimes extending many degrees from the 
head (120°— or a third as much again as the distance 
from the horizon to the zenith — for the comet of 1861), 
and having a real length in some cases exceeding the 
distance of the earth 'from the sun. Ordinarily the 
tail does not attain its full development till after the 
approach to the sun, and the same is true of the jets 
emitted from the nucleus; but the apparent length of 
tail is greatly affected by foreshortening. Its general 
form somewhat resembles a parabola, with the nucleus 
as focus, and having a dark division running along its 
axis; but in many comets it is considerably curved back- 
wards like a plume, and there are frequently secondary 
tails darted out in other directions in the form of a 
fan, besides occasionally a sort of spurious tail directed 
to the sun. Of the causes which produce these tails 
nothing is certainly known, though there seems very 
little doubt that they are due to a repulsive force of 
some kind from the sun, modified by the action of the 
nucleus; but on what this force is exercised seems an 
open question, as it is almost incredible that matter 
could be projected with such an enormous velocity— a 
tail 60 millions of miles long (two-thirds the interval 
between the earth and the sun) having been formed in 
two days in the case of the comet of 1680, and a still 
longer tail in a single day in the comet of 1843. But 
until further observations have been accumulated, it 
appears hopeless to attempt an explanation based on an 
imperfect knowledge of the facts. 

Of late years the spectroscope has been applied to 
several faint comets, the result being that the spectra 
of their heads were found to consist of three bright 
bands, characteristic of carbon in some form. The 
bright comet of 1874 afforded an opportunity which 
had not presented itself since the invention of the 
spectroscope, but very little more was made out in 
this case, for most of the light of the nucleus and bright 
jets in the head was spread out into a coutinuoua spec- 
trum (indicating probably that it is reflected sunlight) 



THEIR SPECTRUM— METEORS. 101 

which almost overpowered the bright bands. The 
light of the tail appeared also to be chiefly reflected 
sunlight, as in the case of the zodiacal light, and there 
our knowledge of this comet appears to end. 

A connection has however in recent years been es- 
tablished between some other comets and certain 
groups of small particles called meteorites, which in 
their journey round the sun sometimes pass through 
the earth's atmosphere with such an enormous velocity 
(35 miles a second on the average) that they are igni- 
ted by the friction of the air, and show themselves to 
us as "falling stars," at a height of about 73 miles on 
the average. Ordinarly these falling stars are com- 
pletely consumed in their passage through the air by 
the time they have got within about 52 miles of the 
earth's surface, being generally extremely minute 
bodies, probably only a few grains in weight; but in 
some few cases considerable masses have fallen to the 
earth after the explosion of a large meteor. Such mass- 
es are composed largely of an ore of iron, and appear 
to be of different character from the ordinary falling 
stars, which generally appear in streams, all the par- 
ticles in any one stream moving in the same direction, 
as is shown by the fact that their paths all radiate from 
the same point of the heavens,which is the " vanishing 
point" of a system of parallel straight lines seen in 
perspective. Thus, about April 20 a large number of 
meteors are seen diverging from a point about mid- 
way between the bright star Vega and a Ophiuchi; 
another stream, known as the Perseids, on account of 
their diverging from the constellation Perseus, is en- 
countered by the earth about August 10; another 
well-marked shower, radiating from y Leonis, and 
hence called Leonids, is met with near November 14; 
and again, on November 27, comes another group di- 
verging from the region lying between y Andromedae 
and Cassiopea. These are only the principal streams, a 
list of more than a hundred well ascertained groups 
having been formed, in each of which all the mem- 
bers are traveling nearly in the same direction. 



102 



PATHS OF METEOR STREAMS. 



Now all this clearly points to an external origin for 
these bodies; and as the supposition that they are cin- 
ders thrown out from the lunar volcanoes affords no 
explanation of their regular recurrence, besides being 
in itself improbable, we are thrown back on the theory 
that they are really minute members of the solar sys- 
tem circulating round the sun in streams. Tins view 
is supported by two facts which have been noted in 
connection with the Leonids: 1. That remarkable 
displays of these meteors occur every 33 years, the 
last having been observed in 18G6 ; and 2. That the 
time when we pass through the thick of the shower 
gets later and later by about a day every 33 years * 
The first circumstance might be explained by suppos- 
ing this group of meteors to revolve round the sun 
nearly in a circle, in a little more than a year or a lit- 
tle less, so that every 33 years the earth caught it up, 
or it caught the earth up, the meeting point of the 
paths of the meteors and of the earth (which are 
somewhat inclined to each other since the meteors do 
not come in the direction of a point in the ecliptic) 
beino- at the place where the earth is on Nov. 14 ; or 
else & by supposing the meteoric stream to circulate 
round the sun in a long ellipse in 33 years. The 
shift of the meeting point of the paths of the earth and 
meteors by 29' corresponding to half a day in 33 years, 
enables us to decide in favor of the last supposition, 
as it is found by elaborate calculations that the attrac- 
tions of the planets would cause exactly such a shift of 
the line of nodes in the case of a long'ellipse. Now the 
period being 33 years, the mean distance, or half the 
lono- axis of the ellipse is found by Kepler's Third 
Law to be nearly that of Saturn, or about 10 times that 
of the earth; but as these meteors move in a very long 
ellipse, they will, when farthest from the sun, be about 

* Half of this lagging is due to a shift of the equinox itself 
along the ecliptic, as will be explained in the next chapter the 
actual shift of the meeting point of the meteors with the earth 8 
orbit, referred to the stars, being only half a day every 66 years. 



MELA'S COMET AND THE METEORS OF NOV. 103 

as distant as Uranus. The direction in which they are 
moving at the time the earth meets them being known, 
their velocity can be calculated from Kepler's Second 
Law, and their path found. When this was done the 
orbit was found very closely to resemble that of the 
first comet of 1866, and a similar investigation in the 
case of the Perseids showed that they moved in the 
same path as the great comet of 186'-^, whilst the April 
star-shower appeared to follow the course of the first 
comet of 1861 ; but the connection between meteors 
and comets was most clearly established in the case of 
the stream of November 27, and Biela's double comet, 
for not only was there an unusual display of meteors 
just about the time the comet was expected to be near 
us, but a comet was actually seen just after wards in the 
southern constellation Centaurus, very near the part of 
the heavens towards which the meteor stream was 
moving, though, unfortunately, cloudy weather at Mad- 
ras (where a telegram predicting the probable ap- 
pearance of the comet in the track of the meteors 
was sent) only allowed the comet to be seen on two 
days, leaving it still an open question whether the 
two heads of Biela's comet were observed on the two 
days respectively or not. Bat however this may be, 
it seems almost certain that on the night of Novem- 
ber 27, 1872, we passed through the outer part of 
a comet, the particles of which appeared as a shower 
of falling stars. There is one noticeable feature 
about some of the meteor streams, especially that of 
Nov. 1-1, viz. : the large arc of their ellipse over which 
they are spread. Thus the dense part of the stream 
of the November meteors takes more than a year to 
pass the meeting place with the earth's orbit, the 
shower of 1867 having been nearly as remarkable 
as that of 1866 ; but though the foremost particles will 
have moved through a large arc by the time the last 
are clear of the earth, this is in the part of the ellipse 
near the sun, whilst when the stream gets to the dis- 
tant part, the arc passed over in a year will be so 
small that all the particles will be tolerably near to- 



104 BRIEF ACCOUNT OF 

gether, and they may then form part of a modern! dv 
compact comet. This branch of astronomy is, how- 
ever, of such recent growth that much is still uncer- 
certain. 

We will now give a brief account of a few of the 
most remaikable comets which have appeared in mod- 
ern times, the records of the ancients being too vague 
to be worth mention here. The great comet of 1680 
has been already alluded to, as being remarkable for 
its near approach to the sun's surface, and also for the 
amazing rapidity with which its tail was formed, ex- 
tending over fully ?0° in the heavens. But this comet is 
chiefly memorable from its having led Newton to the 
conclusion that these bodies move in parabolas, or in 
very long ellipses, a result which he had previously 
shown would follow from the sun's attraction if the 
velocity were greater than that corresponding to the 
same distance from the sun in an elliptic orbit. The 
way in which the velocity at the same distance from 
the sun varies with the nature of the orbit may be 
readily understood by considering the simple case of 
motion in a circle, and supposing the velocity increased 
or diminished. If the body have a greater velocity, 
and, therefore, move over a certain space in less time, 
the sun will not have pulled it quite so far towards 
him, so that it will have run off the circle as it weie, 
describing a curve of larger radius, and thus we gel 
either a long ellipse, a parabola, or even an hyperbola, 
all of which lie outside the circle, just touching it at 
the point where they approach most nearly to the sun. 
If the velocity be about \'i that in the circle, a parabo- 
la will be described, if less than this an ellipse, and if 
greater an hyperbola. ( )n the other hand, if the body 
take longer to move over a certain space, or have less 
velocity than in the circle, the sun will have pulled it 
further towards him, and it will, therefore, describe an 
ellipse, which fal's altogether inside the circle. t< itch- 
ing it only at the point where it is furthest from the 
sun (see figure, page 98). Thus the November mete- 
ors and the comet of 1600 have, when nearest the sun, 



REMARKABLE COMETS. 105 

a velocity greater than that of the earth, whose nearly 
circular path they just touch, and, when furthest, a 
velocity Jess than that of Uranus, whose orbit they 
also nearly touch, but internally. 

The comet. of 1744: deserves mention from its having 
exhibited six tails spread out in a fan shape, in which 
respect it resembled the great comet of 1861, on 
June 30th. It was a remarkably brilliant object, 
being as bright as Jupiter shortly before its perihelion 
passage. In 1769 appeared a bright comet, with a 
tail 100° in apparent length, corresponding to a real 
length of forty millions of miles (half the interval be- 
tween the earth and the sun). The comet of 1811 
was visible for seventeen months, and was accompa- 
nied by a tail more than 100 millions of miles long, 
though its apparent length never exceeded 25°. From 
the length of time during which it was observed the 
deviation from a parabola was quite sensible, though 
the period of revolution appears to be no less than 
three thousand years, the ellipse being so elongated 
that the greatest and least distances of the comet from 
the sun are respectively 420 times and about equal to 
that of the earth ; so that the comet is carried to a 
distance fourteen times that of Neptune ; but this, 
after all, is only about one thousandth part of the dis- 
tance of the nearest fixed star. With regard to the 
comets previously mentioned, the observations are in- 
sufficient to enable us to distinguish with certainty be- 
tween their orbits and parabolas, all that is certain 
being that their ellipses must be exceedingly elonga- 
ted. In 1819 a fine comet appeared, which passed 
over the sun's disc, being seen as a dark nebulous spot. 

The comet of 1843 first showed itself in the northern 
hemisphere by its tail, the head being belowjthe horizon. 
In southern latitudes it was a most brilliant object, being 
actually seen at noon close to the sun on two successive 
days, with a tail several degrees in length, and after- 
wards, when it got clear of his rays, in the evening 
twilight, a tail 65° in apparent length was visible, the 
real length being some 200 millions of miles, or more 



106 REMARKABLE COMETS. 

than the diameter of the earth's orbit. The orbit of 
this comet is the most remarkable known, passing 
within about 100,000 miles of the Sun's surface, but 
whether it is a parabola or an ellipse of moderate or 
even of short period cannot be determined, as the path 
during the period of observation w T as so little curved 
that it could hardly be distinguished from a straight 
line. This arose from our being able to observe only 
that portion of the orbit which is. about 200 times as 
distant from the sun as the perihelion is. 

The next large comet was that of 1858 (DonatiV) 
which was a most beautiful object in the autumn of 
that year, with a tail like a plume, some 60° long, 
corresponding to a real length of more than 50 millions 
of miles. The head in its apparent course passed 
nearly centraiiy over the bright star Arcturus, but 
nothing peculiar was noticed. The most- remarkable 
feature in this comet was the system of parabolic 
arches which formed the head and tail, arranged sym- 
metrically with the nucleus at the focus. Its path ap- 
peared to be an ellipse of about 2,000 years' period, 
making the greatest and least distances from the sun, 
respectively, about 300 times and fths that of the 
earth. 

The comet of 18G1 surprised astronomers in these 
latitudes by its sudden appearance above the horizon, 
though it had been watched for some time in the 
southern hemisphere. On June 30, when it was first 
seen in this country, we were probably actually passing 
through the tail, which w r as then s (i en as a great fan, 
the only unusual appearance noticed being a phospho- 
rescence in the northern sky, something like an auro- 
ra. At this time the head of the comet was some 14 
millions of miles off (nearly GO times the moon's dis- 
tance). On July 2 the tail extended over 120°, reach- 
ing far past the zenith, but its real length was only 40 
millions of miles, and as the comet receded from the 
earth the apparent length rapidly diminished. For a 
few days this comet was a splendid spectacle, and the 
fans of light seen in the head were very hue. Its pe- 



GREAT COMET OF 1881. 107 




[The above diagram shows the head of the great comet of 
1881, as seen on the morning of Jane 24, through the Equa- 
torial telescope at the Dearborn Observatory. Drawn by E. C] 



108 PERIODICAL COMETS. 

riod appears to be about 400 years, the greatest and 
least distances being respectively 110 times and £ that 
of the earth from the sun. 

In August, 1862, a fine comet appeared, the head 
when brightest being nearly equal to a star of the first 
magnitude, with a tail some 25° long, accompanied by 
two secondary tails. From one side of the nucleus 
very remarkable jets of light were emitted, afterwards 
curving round toward the tail, which appears to have 
been, contrary to the general rule, considerably in- 
clined to the direction opposite to the sun; and there 
was a lop-sided character about this comet which pre- 
sented a marked contrast to the symmetry of Donati's 
comet. The orbit of this comet (which is similar to 
that of the August meteors) is an ellipse with a peri- 
od of 120 years, the greatest distance from the sun be- 
ing about 50 times that of the earth (If times that of 
Neptune), and the least distance nearly equal to that 
of the earth. 

Coggia's comet of 1874 was similar to the last 
named comet in general appearance, and in position 
in the heavens. The head was remarkable for inter- 
secting parabolic arches of light, which gave it a very 
beautiful appearance in a large telescope. 

No less than seven comets were observed in 1881. 
The most remarkable of these flashed suddenly into 
our view June 23, having passed between us and the 
sun. When first seen in the northern hemisphere it 
was less than 30,000,000 miles from the earth. The 
head seemed to consist of two masses, but they were 
connected by a well defined bar, or bridge, of light. 

Among the periodical comets, Halley's is the most 
famous, both for its size and for the regularity of its 
apparitions at intervals of about seventy-six years; 
twenty-two having been recorded between b. c. 12 
and a. d. 1835. This was the first comet of which 
the return was predicted, Halley having found the 
orbits of the comets of 1531, 1C07, and 1G82 to be 
very similar, from which he concluded that they 
were really three apparitions of the same comet, 



REMARKABLE COMETS. 109 

which might be expected to return about the be- 
gining of 1759, the period from 1607 to 1682 being- 
shorter than the average through the attraction of 
Jupiter. At its last appearance in 1835 the comet 
was by no means so striking an object as on former occa- 
sions, when it filled Europe with alarm; but though it 
appears to have lost much of its glory, it will doubtless 
be a conspicuous comet at its next return in 1910. 
This comet approaches the sun within fths of the 
earth's distance from him, and recedes to a distance 
exceeding by one-sixth that of the planet Neptune. 




coggia's comet. 

Another very regular periodic comet is that known 
as Encke's, of which above twenty returns, correspond- 
ing to thirty revolutions, have been observed since 
1786, the period being not quite 3^- years. This is a 
small comet, barely visible to the naked eye, even un- 
der favorable circumstances, and usually destitute of 
a tail ; but much interest attaches to it from the fact 
that its period has diminished by about two days since 
its first appearance. This has been supposed to afford 



110 PERIODICAL COMETS. 

evidence of the existence of a very rare resisting me- 
dium in space, which, by diminishing the comet's ve- 
locity, would make it describe a smaller orbit with a 
greater angular velocity. Its distance from the sun 
ranges from that of Mercury to four-fifths that of 
Jupiter. Biela's comet, with a period of 6£ years, is 
remarkable from the circumstance of its orbit inter- 
secting that of the earth, a collision having probably 
oceunedin 1872, November 27, as already mentioned. 
A still more remarkable fact about it is, that inl846 
it divided into two distinct comets, which separated 
to a distance of about three-quarters that of the moon 
from us ; an interval which, at the next apparition in 
1852, had increased to about six times the moon's 
distance, with a difference of fifteen days in the periods 
of the two heads. Neither comet has been cer- 
tainly seen since, though they were due in J 859, and 
again in 1866, and if either of them caused the mete- 
or shower of 1872, November 27, they must have been 
retarded six months in the interval since the last ap- 
pearance in 1852. Biela's comet was first observed 
in 1772, but has only been seen at six of its returns 
since that time. Its greatest and least distances from 
the sun somewhat exceeded those of Jupiter and Ve- 
nus respectively. 

The other periodical comets are given in the list at 
the end of this work, with a few particulars about 
their orbits. It will be noticed that the greater num- 
ber of these reach a little beyond that of Jupiter, and, 
further, the plane of the orbit is so adjusted with ref- 
erence to the direction of its length, that each comet 
passes very near Jupiter, who may therefore, by his 
attraction, possibly have converted its parabolic orbit 
into an ellipse of short period. This is what actually 
happened in the case of Lexell's comet, which was 
found in 1770 to be moving in an ellipse of 5£ years' 
period, through its having passed very close to Jupiter 
in 1767, and before it was again seen the orbit was 
again completely deranged by another and still closer 
approach to the same planet, which appears to have 



ORIGIN OF COMETS. Ill 

greatly increased the least distance from the sun, car- 
rying the comet altogether beyond the range of our 
vision, even when nearest. This comet approached 
the earth in 1770, within six times the distance of the 
moon, without causing the slightest alteration of our 
course, though the comet's path was much disturbed. 

[The remainder of this chapter is part of the Warner- 
prize essay on comets, written by Prof. Lewis Boss, of 
Albany, N. Y.] 

The balance of testimony seems to favor the suppo- 
sition that comets originate outside the solar system.' 
The planets move in nearly circular orbits about the 
sun; and no one has been able to show why comets, 
if they have the same origin, should move in elongated 
orbits, entirely differing from those of planets. 

Let us suppose, however, that all comets must have 
taken their origin in some primeval nebula from which 
a solar system has been evolved. It has been shown 
that the velocity of a comet may be so much increased 
by the disturbing action of a large planet, that it may 
escape from the control of the sun, and be projected 
into the illimitable regions of space. Thus freed, it 
will go on in a nearly straight line forever; unless, 
perchance, some powerful source of attraction, like 
another sun, lying near its path, arrests its flight. The 
possibility of such an occurrence is by no means im- 
aginary. At least, one comet (Lexell's, 1770) is sup- 
posed with good reason to have undergone that fate. 
There is every reason to believe that the same thing 
may have happened in other cases. 

AH argument drawn from observation and reflection 
proves that the stars which surround us on all sides are 
remarkably like our own sun, Some of them are even 
larger and more powerful than he. Reasoning from 
analogy, we must suppose that these suns are also at- 
tended by comets. Hence, we are led to the conclu- 
sion that uncounted myriads of comets projected forth 
from millions of suns, during countless ages past, are 
now flying through space in every direction — restless 
messengers from star to star. By mere chance some 



112 NUCLEUS OF A COMET. 

of these bodies must come under the sun's far-reach- 
ing power and be drawn into our planetary system. 

The mass (quantity of matter) of comets is conced- 
ed to be very small in comparison with that of the 
earth. How small it is we can not say. No comet 
has been found large enough to exert a sensible at- 
traction upon any celestial body found in its vicinity. 
This fact confirms the conclusion derived from tele- 
scopic examination, that the real, solid nucleus, if it 
exists, must be extremely small. 

It is certain that no body entirely gaseous could 
exist in space. The conditions for the stability of 
liquid bodies in their practical application to the ex- 
planation of cometary phenomena, are extremely com- 
plicated; since they are closely associated with the 
unknown element — mass of the comet — solar radiation. 
and absolute temperature of space. It would also be 
extremely difficult to show how a swarm of small bod- 
ies could be preserved in a state of equilibrium, or 
resist the tremendous tidal action to which it would 
be subjected in the vicinity of the sun. In fact, we 
must view the conversion of a comet through some 
unusual catastrophe, into such a swarm, as the sure 
precursor of approaching dissolution. ( )n the wht >le, it 
is probable that there is a solid or partly liquid body 
near the centre of the comet. This body is more like v 
to consist of an aggregation of loosely cohering pieces 
or particles, than of a single firmly united mass. 

Owing to the smallness of their attractive force, 
comets can not retain a sensible atmosphere. Tli:> 
conclusion is confirmed by telescopic observation. 

If, now, we suppose the nucleus to be approaching 
the sun, it will eventually reach a point where the 
liquid or other volatile matter on the " sunny M side 
commences to evaporate and be diffused about the 
comet. Without following the consequences of this 
evaporation into details, one can imagine for himself 
how the appearance of central condensation, of the 
streaming jets, and of the nucleus heavily obscured by 
vapors, might be produced. 



HOW THE TAIL IS FORMED. 113 

To account for the backward curvature of the jets 
and the peculiar form and direction of the tail, we 
must look for some additional force. In all probabili- 
ty fthis force resides in the sun, and is directly opposite 
in its effects to the power of gravitation. But since 
the body of the comet obeys the law of gravitation 
with sufficient fidelity, we must find a repulsion which 
sensibly acts only on the molecules of gas or vapor. 

The only force suggested by experience as compe- 
tent to these requirements is that of electrical repul- 
sion. Anyone can prove for himself that two bodies 
similarly electrified mutually repel each other. We 
know that the earth, through effects of constant evap- 
oration and other causes, is to some extent an electrical 
body. For the same reasons, we should expect com- 
ets to be electrified in a much higher degree. The 
sun itself certainly exerts an influence upon terrestrial 
magnetism. Violent commotions on his surface have 
occurred at the same time with unusual disturbances 
of the magnetic needle. Electrical repulsion acts in 
proportion to surfaces and not to volumes. On parti- 
cles of matter in a state of infinitesimal subdivision it 
might act most powerfully, while not affecting a large 
mass to an appreciable degree. 

If, then, we suppose the sun and comets to be suffi- 
ciently and similarly electrified, we have the force 
necessary to produce the backward curvature of the 
jets, and to drive off the smallest and probably the 
outermost molecules of the coma to form the tail. 
Since, according to our hypothesis, very little matter 
can be given off from the shaded side of the nucleus, 
we readily perceive why the tail should be hollow in 
appearance. 

The orbit of the moving nucleus being curved, it is 
evident that the particles driven off at any time with 
less than infinite velocity, would continually fall more 
and more behind the prolongation of a line through 
the sun and comet — just as has been observed. If the 
matter contains molecules, varying considerably in 
'size, the larger ones would be driven off with less veloci- 



114 MULTIPLE TAILS. 

ty. These would curve "backward more than would 
the lighter molecules driven off at the same time, and 
so we have multiple tails. Elaborate examinations 
of their average observed direction and form suggest 
that each class may be composed of chemical elements 
peculiar to itself. We may even venture to suppose 
that the tail of greatest velocity and least inclination 
is composed of hydrogen. The second type may con- 
tain carbon, with or without other elements ; and 
among those of the third, chlorine would most likely 
be found. 

It is a common error to suppose that this hypothesis, 
as in the formation of the tail, requires a repulsive 
force of inconceivable power. The straightest tails 
which have been observed are accounted for by sup- 
posing a repulsive force not much greater than twelve 
times the sun's attractive power. The tails most fre- 
quently seen (scimeter-like in form) may be produced 
by a force about one-ninth of that amount, which is 
but little more than sufficient to overcome the attrac- 
tion of gravitation. 

It will be seen that it is equally erroneous to sup- 
pose any great amount of material wasted in the for- 
mation of the Jail, when one reflects upon the trans- 
cendent brightness of its structure. 

The| influence of comets upon the earth is in all 
probability quite insignificant. They may, like the sun, 
affect the earth's magnetic condition, and thus to some 
extent, possibly, its meteorology. No such effect has 
e.ver been perceived. In spite of some chance coin- 
cidences between the apparitions of great comets and 
remarkable public events, no well-informed person 
now believes that there is any real connection between 
them. By a liberal and credulous interpretation of 
any frequently-occurring celestial phenomenon, similar 
coincidences could be shown. 

1 \*% When a comet is converted into meteoric bodies, 
which impinge upon the earth's atmosphere, there is 
some direct though probably minute effect. Some 
have thought that a sensible portion of the heat which * 



COMETS AND METEORS. 115 

the earth receives is generated in this way; but the 
weight of scientific opinion seems to be against that 
hypothesis. The impact of meteors upon our atmos- 
phere must add some matter to it, and this is probably 
in the form of dust. This may be the origin of the 
so-called cosmic dust, which has been collected at sea 
in recent times. The finer particles of it may have 
some influence on cloud formations, and other meter- 
orlogical phenomena; but all this is merely conjecture. 

A more remote effect may be sought in the possible 
fall of meteors and comets upon the surface of the 
sun. Owing to his vast bulk, the sun would attract 
an immense number of these bodies; but it is quite 
certain that their effect upon the sun's heat is insig- 
nificant. It is now generally admitted that we must 
look for the origin of the sun's heat in a constant, 
though to us imperceptible, shrinkage of his vast bulk. 

Some connection between the frequency of sun- 
spots and comets has been rather vaguely suspected. 
Were the search for comets systematically pursued 
with equal persistence for a long period, we might 
have some data for the formation of a sound opinion. 
Yet it would still be an open question whether comets 
cause the spots, or whether greater activity of the sun 
tends in some way to render comets brighter, so that 
more will be visible; with probability in favor of the 
latter supposition. 



CHAPTER VI. 

To the naked eye on a fine night, the stars bewilder us 
by their number, making it impossible to give each of 
them a separate name, on which account the practice 
was adopted of grouping them into constellations, 
named from some fanciful resemblance to or con- 
nection with men or animals. In early times the stars 
were distinguished by their position in the constella- 



116 THE STABS— THEIR NUMBER. 

tion to which they belonged; but afterwards, as the 
less conspicious stars began to be observed, those in 
each constellation were distinguished by the successive 
letters of the Greek alphabet in the order of their 
brightness, so that a Aurigae would be the brightest 
star in the constellation Auriga, ft Auriga? the next 
brightest, and so on, numbers being used when the 
alphabet was exhausted. For the stars which have 
been observed only in modern times, it has, however, 
been found more convenient to give the name of some 
catalogue in which the star's place is given, and the 
number corresponding to the star in that catalogue, 
and thus every star that has ever been observed is dis- 
tinguished. When it is stated that there are cata- 
logues which contain 100,000 stars, the necessity for 
careful nomenclature, for the smaller stars at any rate, 
will be at once apparent. With the naked eye some 
3,500 stars are to be seen in the United States, and of 
these only about 2,000 at any one time; the number 
thus visible in the whole heavens, including the 
southern portion, always below our horizon, is only 
about 10,000; but when the telescope is applied the 
multitude of stars is enormously increased with every 
increase in the size of the telescope, and very soon gets 
quite beyond our powers of counting, even. Every 
gradation of brightness is found in the heavens (except 
in the case of the very brightest stars), but for con- 
venience, the stars visible to the naked eye are roughly 
classed in six orders of brightness, or magnitudes, as 
they are called, certain very bright stars, nineteen or 
twenty in number, being called first magnitude (though 
by no means exactly equal in brightness); after these 
come about 60 stars of the second magnitude; about 
120 of the third, and so on; but though these classes 
do very well to give an idea of a star's brightness, 
greater accuracy is in many cases required, and thus 
half magnitudes are introduced, a star of the 3£ mag- 
nitude being intermediate in brightness between the 
third and fourth magnitudes. In delicate observa- 
tions of changes in the brightness of certain stars, 



MAGNITUDES— THE CONSTELLATIONS. 117 

tenths, or even hundredths of a magnitude are used to 
express the relative brightness of the star as compared 
with those of the standard magnitudes, so that instead 
of speaking of a star roughly as of 3|- magnitude, we 
might call it 3.6, or perhaps more accurately, 3.62; 
Below the sixth magnitude we have magnitudes only 
visible in the telescope, stars of any one magnitude 
being 2^- times as bright as those of the magnitude 
below; that is, two stars of the eighth magnitude very 
close together would not be quite so bright as a single 
star of the seventh magnitude, whilst three would be 
brighter. With the first srx magnitudes this relation 
does not hold exactly, the classification being some- 
what arbitrary; indeed different observers have varied 
considerably in their scale, though agreeing pretty 
well in the two extremes, and making 100 sixth mag- 
nitude stars equal in brightness to an average first 
magnitude, a relation which agrees very nearly with 
the scale of %\ for each magnitude. 

We shall now endeavor, with the help of the Key 
Map (frontispiece),* to enable the reader to recognise 
the most conspicuous stars, in which he will be much 
assisted by the grouping into constellations, conven- 
tional though it is. In the first chapter mention was 
made of the pole star ; but this star is not very con- 
spicuous, and we did not point out how to find it 

* This map represents part of the imaginary sphere of the 
heavens as it would be seen on a moonlight night (when the 
brighter stars only are visible), from a point at a distance of 
half the radius beyond the south pole of the sphere, stars below 
the fourth magnitude being omitted. The southern constella- 
tions, such as Scorpio, Sagittarius, &c, are necessarily much 
distorted, it being impossible to represent properly a spherical 
surface on a sheet of paper. The principal stars are distin- 
guished .by letters of the Greek alphabet, and the constellation 
to which any star belongs will be found on that side on which 
the letter is placed. The bottom, left hand, top, and right 
hand, correspond respectively to the southern part of the 
heavens at 10 p. m. in autumn, winter, spring and summer; 
the opposite side being in each case below the northern horizon, 
which passes at a distance of 42° from the Pole for Chicago. 



118 GREAT AND LITTLE BEARS— CASSIOFEA. 

readily. On any fine night, if we turn to the north (so 
as to have our back to the sun at noonday) we shall 
see seven bright stars marking the constellation of Ursa 
Major (the Great Bear) — which will be found above 
the centre of the map and a little to the left — the two 
lower stars of which point pretty nearly to the 
pole star (at about six times the distance between 
them), and are therefore called the Pointers. In winter, 
in the evening, these stars are below the pole and low 
down in the north, but in summer they are above the 
pole and nearly overhead. As already explained, the 
stars preserve the same positions among themselves, 
swinging as a whole round the pole, and thus the seven 
stars of the Great Bear will be readily recognized by 
the form of the constellation, however it be turned 
with respect to us. The pole star, found in this way, 
will be seen to form part of a somewhat similar though 
smaller constellation of seven stars, hence called Ursa 
Minor or the Little Bear, which never alters its height 
much, swinging round the tip of its tail (the pole star). 
A line carried from the Great Bear's tail through the 
pole star, and as far again beyond, will strike a con- 
spicuous group of five principal stars, arranged some- 
thing like the letter W, which is known as the constel- 
lation Cassiopea, and forms a convenient land mark in 
the heavens. It will be understood that in this and 
other constellations only the principal srars are alluded 
to, though there are a large number of smaller stare 
visible to the naked eye, wliilst the telescope reveals 
almost countless multitudes. Carrying a line from tin- 
pole through the most westerly of the stars in I 
opea, and as far beyond, we come upon a large squard 
formed by four bright stars, three of which are in the 
constellation Pegasus, whilst the fourth or north-east 
star of the square is a Andromeda?. Each side of this 
square is about 15° in length, or nearly three times 
the distance between the Pointers, which are a little 
over 5° apart. The other two conspicuous stars in 
Andromeda, ft and ^, form a sort of tail to the north- 
east of the square, and still further eastward is the 



NORTHERN CONSTELLATIONS. 119 

constellation Perseus. A line through the two wester- 
most stars of Cassiopea, fj and «, will strike y Andro- 
medae, and about as far beyond will pass a little west 
of the Pleiades, a cluster of stars of which six are or- 
dinarily visible to the naked eye (though several 
more may be seen on a very fine night), whilst nearly 
15° further is a V-shaped cluster, called the Hyades, 
having a first magnitude star, Aldebaran, at one tip. 
Both these clusters belong to Taurus, the Bull, which 
is one of the constellations of the Zodiac, or belt of the 
heavens, extending 8° on either side of the ecliptic, 
and including the paths of all the principal planets, 
which are never far from the ecliptic. The Zodiac is 
divided into twelve constellation?, each occupying 
about 30° — Aries, Taurus, Gemini, Cancer, Leo, Virgo, 
Libra, Scorpio, Sagittarius, Capricornus, Aquarius, 
Pisces — the order given being that in which the sun 
passes through them, or from west to east. Aries has 
two bright stars, a and /?, 4° apart, and nearly midway 
between the Pleiades and Pegasus; in Gemini are two 
leading magnitude stars, Castor and Pollux, north of 
the ecliptic, about 50° nearly due east of the Pleiades; 
Cancer is not a conspicuous constellatior, but Leo will 
be recognized at once by six stars in the shape of a 
sickle, the first magnitude star Regulus forming the 
handle, 40° south-east of Castor and Pollux. Virgo 
contains one first magnitude star, Spica (the ear of 
con:), 10° south of the equator and more than 50° from 
Regulus. The remaining constellations in the Zodiac 
are not conspicuous, though Scorpio has several bright 
stars, including one of the first magnitude, Antares. 
It will be remarked that several of the brightest stars 
referred to above have names of their own, indepen- 
dent of the constellation they are in. This is a relic 
of the old practice of naming, or rather describing, 
the individual stars, the words being generally cor- 
ruptions of the names given by the Arabian astron- 
omers to define the position of a particular star in the 
constellation, and these are still retained, though the 
star is also known by its proper Greek letter, coupled 



120 NORTHERN CONSTELLATIONS. 

with the name of the constellation ; thus Antares is 
also called a Scorpii; Aldebaran, a Tauri, and so in 
other cases. 

Among* the constellations north of the zodiac, 
Bo5tes is distinguished by the brightest star of the 
northern hemi phere, Arcturus, which is nearly pointed 
to by the last two stars of the Great Bear's tail ; 20° 
north-east of Arcturus, is the constellation of the 
Northern Crown (Corona), composed of a tolerably 
perfect wreath of stars. A line from the tip of the 
Great Bear's tail through the Crown, and carried as 
far beyond, will strike two stars 5° apart, a Herculis 
of the third magnitude, and a Ophiuchi of the second, 
the other stars of the constellation Hercules lying to 
the north of these two, and therefore east of Corona. 
whilst those of Ophiuchus lie to the south. Still 
further east of the Crown is the very bright first mag- 
nitude star, Vega or a Lyra?, which with a small star 
near forms a sort of pendant to a lozenge of four Stars, 
and is to be seen not far from the zenith in the 
autumn evenings. In the direction of the lozenge 
(*. e. t south-east,) lie three bright stars, some 3° apart, 
forming a line pointing to Vega, which is 35° distant: 
these stars are r, a, and ft Aquilae, and will easily be 
identified by their appearance. The southern side of 
the square in Pegasus also points to them at a distance 
of three times its length, passing just north of the 
bright star « Pegasi on the way. The north-west 
diagonal of the same square will strike (at nearly 
twice the distance beyond) a Cygni, the lucida of a 
constellation formed by a zigzag line of bright stars 
i mining N. W. and S. E., and representing the wings 
of a swan flying, while the outstretched head is shown 
by a third magnitude star, ft Cygni, some 20° to the 
S. W. Continuing our course eastward, we get to 
Pegasus and Andromeda, already noticed ; then we 
have Perseus, in which there are two bright stars, 
Mirfak and Algol (a and ft Perse i), of "which the 
former is on a line through ft and y Andromeda;, and 
thus forms the tip of the tail to the square of Pegasus, 



OBION AXD THE DOG STAR. 121 

whilst ft Persei forms the apex of an obtuse angled 
triangle with y Andromeda? and a Persei. A line 
from the square of Pegasus through y Andromeda? 
leads to one of the brightest northern stars, Capella 
(a Auriga?), with ft Auriga? a little to the east, between 
which and Bootes there are no very conspicuous stars. 
Of the southern constellations visible in these lati- 
tudes, by far the most striking is Orion, which is on 
the meridian about ten in the evening in the month 
of January, lying in the direction of a line from the 
Pieiades through the Hyades, but there can be no 
difficulty in identifying this magnificent assemblage 
of stars, the most beautiful feature in the winter sky. 
Four bright stars forming a quadrangle represent the 
shoulders and legs of Orion: Betelgeuse and Rigel (a 
and ft Orionis) at the N. E. and S. W. corners re- 
spectively, being both of the first magnitude ; the 
head is indicated by a small triangle of stars, and 
three second magnitude stars in a diagonal line in the 
middle of the figure form the belt, which has a dagger 
of three other stars hanging from it. The line of 
Orion's belt points to the brightest star in the whole 
heavens, Sirius, or the Dog Star ( a Canis Majoris), 
shining with a splendor which is something lire nine 
times that of Vega. Another very bright star, ough 
much inferior to Sirius, remains to be noticed, P± n, 

or a Canis Minoris, which, with its companion ft l 
Minoris, is found by carrying a line from the Pe 
through Castor and Pollux nearly as far as the equator, 
where it will be picked up some 25° east of Betel- 
geuse. 

In all that precedes we have followed the constella- 
tions in an eastward direction, taking them as they 
successively come to the meridian, but it must not be 
forgotten that only a portion of the heavens can be seen 
at once on any one night, however long we watch ; for at 
any particular season of the year many of the constella- 
tions will be above the horizon only in the daytime, 
and will, therefore, be invisible to the unassisted eye. 
It will be useful, however, to indicate roughly the prin- 



122 MILKF WAY— CLUSTERS— NEBULJE. 

cipal constellations which will be on or near the merid- 
ian at the four seasons of the year about ten o clock 
in the evening ; if the appearance of the heavens be 
required for any other hour, it is only necessary to 
reckon every two hours later in the time we take, as 
equivalent to taking the positions of the stars for ten 
o'clock a month later, and conversely for the earlier 
hours of the evening— thus the positions at midnight in 
December will be the same as those at ten o'clock m 
January, whilst the appearance of the heavens at six 
o'clock will be the same as at ten o'clock in October. 
Takino- ten o'clock in the evening, then, as our time ot 
observation, we shall have in spring, Regulus on the 
meridian, Ursa Major nearly overhead, the Pleiades 
and Hyades, Orion and Sirius setting, Capella high up 
in the west, and Aroturus with the Crown in the east; 
at midsummer the Crown is on the meridian, with Arc- 
turus a little west of it, and Regulus setting, while 
Veo-a, Aquila, and Cygnus are in the east, and Ursa 
Major in the north-west ; in autumn, Pegasus is near 
the meridian, Vega and Aquila west of it, and Aretu- 
rus with the Crown setting, whilst in the east we have 
Perseus and Capella, with the Pleiades and Hyades 
rising ; at midwinter the latter are on the meridian, 
with Orion and Sirius in the south-east, Pegasus in the 
west, Cygnus low down in the north-west, with Cassi- 
opea higher up; Capella is nearly overhead, and in 
the east are Castor and Pollux, Regulus (rising), and 
further north Ursa Major. These are only rough in- 
dications, but, with what has been given before, they 
will be sufficient to enable any one to identity the 
principal constellations; in fact for this purpose it will 
be enough to remember that about ten O clock we havr 
on the meridian, in spring, Regulus with its sickle of 
stars; at midsummer, Areturus and the Crown; in 
autumn, the square of Pegasus ; and in winter, the 
Pleiades and Hyades, all at about the position ot the 
sun at noon in summer. 

There is one conspicuous object, the milky way, 
which adds greatly to the beauty of the heavens 0:1 a 



THEIR SPECTRA. 123 

moonless night, especially in autumn. This belt of 
nebulous light forms an irregular zone with many 
patches and offshoots, but in the main coinciding with 
a great circle through the solstices inclined about 60° 
to the equator. With the telescope this bright band 
is found to consist of a vast multitude of stars, too faint 
to be individually perceived by the naked eye, and in 
some cases so close together that a powerful telescope 
is required to show the separate stars. 

Such aggregations of stars are called clusters, and 
are found of every degree of condensation, but gener- 
ally circular in form, if the more scattered ones be 
excluded. Many of them are most beautiful objects, 
even in small telescopes, but powerful instruments are 
required to show the more compact clusters in all 
their glorv. Among the coarser clusters the Praesepe' 
in Cancer (nearly equi-distant from Castor, Procyon, 
and Regulus), and one in Perseus at about a third of 
the distance from d Cassiopeae to a Persei, are visible 
to the naked eye as small nebulous objects, which have 
been occasionally mistaken for comets by beginners. 
As we pass to clusters more and more compact, we get 
by insensible stages to the nebulae, which are for the 
most part nothing but clusters, that can only be re- 
solved into stars by the most powerful instruments of 
modern times. When first attention was directed to 
, the subject, it was thought there was a difference in 
kind between the clusters and the nebulae, but as 
inore and more powerful instruments were made, 
and nebulae previously held to be irresolvable were 
separated into their component stars, this idea was 
gradually abandoned, and the distinction between 
clusters and most nebulae became only one of de- 
gree. But there were a few nebulae which still 
defied even the most powerful telescope, and the 
question of the constitution of these objects was left 
to be settled by the spectroscope, which revealed a 
spectrum consisting of three bright lines. Now in 
the second chapter we have already explained that a 
spectrum of that kind indicates glowing gas, whilst a 



124 NEBVL.E 

heated solid gives rise to a continuous spectrum, as 
in the case of the sun, of stars, and of the ordinary 
clusters. These nebulae, then, cannot be collections of 
stars, but must be masses of glowing gas, though what 
that gas is remains an open question. 




STAR CLUSTER AND NEBULAE. 

Two of the nebulae can be seen by the unassisted 
eye, one being in the middle of Orion's dagger, where 
it looks like a blurred star, and the other about a 
third of the distance from ft Andromedae to ft Cassi- 
opeae. The former of these, which from its spectrum 
appears to be gaseous, is an irregular shaped mass, 



AND STAR CLUSTERS. 125 

without any decided boundary, in the midst of which 
is a pretty bright multiple star, with others scattered 
about; whilst the nebula in Andromeda, giving a con- 
tinuous spectrum, is on the contrary of pretty definite 
shape, presenting the appearance of a long oval, in- 
creasing considerably in brightness towards the cen- 
tre. This nebula, however, has not yet been resolved 
into stars, though the spectroscope indicates that it is 
not composed of gas, unless indeed it be in a very 
dense state. On the other hand, another nebula, which 
shows the bright lines, due to glowing gas, has been 
resolved into minute points of light, which, however, 
must be something different from stars in their ordi- 
nary state. This nebula, midway between /3 and y 
Lyra?, is ring-shaped, and one of the most extraordi- 
nary objects in the heavens, even with a moderate 
telescope; it is one of a very small class, the ellipti- 
cal nebulae being far more common. The planetary 
nebulae form another remarkable class, presenting 
round uniform discs like those of planets, and giving 
the spectrum of glowing gas; allied to these are the 
nebulous stars, which are occasionally met with. 
There are also the strange spiral nebulae, or rather 
clusters, of which one near the tip of the Great 
Bear's tail is the finest example; but perhaps the 
most remarkable objects are the double nebulae, the 
finest of which is the " Dumb-bell" nebula in Vul- 
pecula, composed of two oval masses of incandescent 
gas in contact. Altogether more than 5,000 clusters 
and nebulae have been observed, though the vast 
majority of them are beyond the reach of ordinary in- 
struments. The clusters are almost entirely confined 
to the Milky Way, whilst the nebulae appear to avoid 
this zone, being especially collected in the constellation 
Coma Berenices and the adjacent parts of Virgo in the 
northern hemisphere, and in the two Magellanic 
clouds in the southern. 

The systems of stars which form the clusters and re- 
solvable nebulae are found in every stage of conden- 
sation, passing from groups like the Pleiades through 



. 12 6 NEBULAR THEORY. 

the globular clusters and oval nebulae to masses of stars, 
like the spiral nebulas and others of less regular shape ; 
but there seems to be a break when we get to the gas- 
eous nebulas, which is to a certain extent explained by 
Laplace's Nebular Theory. On this hypothesis the 
solar system was originally a gaseous nebula rotating 
about its centre, which in the process of condensation 
assumed something of a spiral structure, each whorl of 
the spiral forming a sort of ring, which attracted the 
matter in its neighborhood, and gradually condensing 
broke up into several portions. These ultimately 
coalesced under the influence of their mutual attrac- 
tions, and formed a planet rotating about its axis in the 
same direction as that of the nebula, since the gas 
which came from outside the ring would have a 
greater velocity eastward, and that from inside a less 
velocity eastward— which, as compared with that of 
the ring, would be equivalent to a relative velocity 
westward; so that as referred to the centre of the 
planet the outer particles would be moving eastward, 
and the inner westward, which is in facta rotation 
from west to east. The greatest condensation would 
take place at the centre, where a large central sun 
would be formed that would attract to itself nearly all 
the matter in its neighborhood, so that only small 
planets would be formed near it. Nearer the bound- 
ary of the nebula the attraction of the central sun 
would be less felt, and the planets. formed there would 
be able to attract to themselves more of the nebulous 
matter, becoming themselves centres of smaller nebu- 
lar systems, from which the satellites would be formed 
in the same way as the planets in the large nebula, 
circling in the same direction round a large central 
planet, such as Jupiter or Saturn. The sphere of at- 
traction of the larger planet being greater, the inter- 
vals between the orbits would increase with increasing 
distance from the sun, and this would be exaggerated 
by the decreasing density of the nebula as we proceed 
outwards. 

Though this is only an hypothesis, changes in the 



DTSTAXCES OF THE STABS. 127 

solar system of this Dature requiring countless ages for 
their working out, and being therefore beyond the 
reach of any known methods of observation, it appears 
highly probable, from what is known of the zodiacal 
light, that our sun is really a nebulous star, while the 
connection between comets and meteors serves to show 
that phosphorescent gas may readily pass into the form 
of minute bodies, which are no smaller in proportion 
to the minor planets than those are as compared with 
such bodies as Jupiter or Saturn. But though we can- 
not detect any changes going on in the solar system, 
or up to the present time in any of the nebulas which 
are supposed to represent its primitive condition, 
we find changes in going from one nebula to another 
which correspond well with what may be supposed to 
be taking place in any particular nebula in the 
course of millions of years. Thus there are gaseous 
nebulae of various forms, some of them to all appear- 
ance physically connected with stars; there are resolv- 
able nebula? composed of very minute stars, and there 
are clusters of larger stars, in which the process of con- 
densation appears to have been carried a step further, 
whilst the spectroscope reveals to us stars which seem 
to be in a transition state, their light being derived 
from glowing gas, though in this case it is hydrogen, 
not the unknown substance of the true nebulae. But 
we must not push the analogy between our system and 
the nebulae and clusters too far, for there are points of 
difference; and it would seem more probable that ours 
is only a secondary system, forming part of some en- 
ormous cluster. 

This much, however, is tolerably certain, that our 
sun is really one of the stars, and that the earth and 
other planets would be all t>ut invisible even from the 
nearest of them, careful observations showing that the 
earth's orbit at that distance is apparently not more 
than one second across. If, then, we view the star 
from opposite points of the earth's path, there will be 
this small shift of V\ and this is our only means of 
finding the star's distance, for clearly any parallax 



128 DISTANCES OF THE STARS. 

from different stations on the earth will be quite insen- 
sible. It is not necessary that the two observations at 
opposite parts of the earth's orbit should be made at 
the same time, which would evidently be impractica- 
ble, but it is sufficient to determine very carefully the 
star's position, and then to wait six months, when the 
earth's motion will carry us to the other side of her 
orbit ; the shift of a star caused by this motion of the 
earth in her orbit is called annual parallax, represent- 
ing the difference between the positions of the star as 
seen from the sun and earth, and may be determined 
in two ways : — 1. By measures of absolute right as- 
cension and declination ; 2. By measures of angular 
distance from neighboring stars. The first method is 
liable to errors as large as the quantity we are seek- 
ing, but it has been applied with success to the bright 
Southern star a Centauri, giving an annual parallax 
of half a second — the largest yet found — the whole 
shift for opposite parts of the earth's orbit being 1 ", 
corresponding to a distance 400,000 times that of the 
sun, or some 13,000 times that of Neptune. The only 
satisfactory way of expressing this enormous interval 
which separates us from the nearest fixed star, is by a 
reference to the velocity of light, which, traveling at 
the rate of 186,000 miles in a second, takes years to 
reach us, having passed Neptune only 4 hours be- 
fore. Thus in looking at this star we only sec its state 
6 years ago, and this, be it remembered, is one of the 
nearest fixed stars ! The second method may be com- 
pared to the determination of the distance of Venua 
by means of her transit across the sun, the relative 
shift being measured ; but in that case we know the 
relative distances, whilst with the stars all we can do 
is to select such stars for reference as we consider to 
be probably at a far greater distance than the star in 
question. Thus, if two stars be nearly in a line, but 
one of them far behind the other, they will bt 
apparently close together, and a shift in our position 
will alter the apparent distanc \ between them, bring- 
ing them more nearly in a line or throwing them fur- 



ABSOLUTE AND RELATIVE PARALLAX. 129 



ther out. In any case, if such a shift be found, we 
know that the earth's orbit must appear of at least this 
size as seen from the star which is shifted, so that 
the distance cannot be more than would correspond to 
this, and may be considerably less. The following list 
gives the parallax of the stars in which any shift has 
been observed, together with the magnitude of the 
star, from which it will be seen that the brightest stars 
are by no means the nearest to us in all cases : — 



First Method. 


Mag. 


Absolute 
Parallax. 


Journey 

of Light in 

Years. 


<x Centauri 


1 

1 
1 
1 

6J 


0-5" 

0-5 
0-2 
0-2 
1-0 (?) 


6 


fi Centauri 


6J 


Procyon 


16 


Arcturus 


16 


Groombridge 18c!0 


3|(?) 


Second Method. 


Relative 
Parallax. 




61 Cygni 


5J 

4 

Si 

9 

1 

1 

4* 

2 
6i 


0'4" 

0'4 

0-25 

0-25 

0'2 

0-2 

0-2 

o-i 

1 (?) 


8 


7} Cassiopeae 


8 


Lalande 21258 


13 


Oeltzen 17415 


13 


Vega 


16 


Sirius. 


16 


70 Ophiuchi 


16 


Polaris 


32 


Groombridge 1830 


32 (?) 



In the case of the smaller parallaxes the results are 
very uncertain; and this is especially so with Groom- 
bridge, 1830, for which a negative parallax relatively 
to one star in its neighborhood has been found, indica- 
ting that the star in question is nearer to us than Groom- 
bridge, 1830 — but not much confidence is to be placed 
in this result. 

It may seem strange that some of the small stars giv- 
en above should have been selected for observation, 
but attention was called to them by the discovery that 

9 



130 STARS IN MOTION. 

they were moving among the other stars at a rate 
which, though very small, was far greater than that 
of most other stars, from which it was concluded that 
they were probably much nearer to us. This state- 
ment may startle a reader who is used to the phrase 
fixed stars, but really the motion is so small that very 
accurate observations, separated by a long interval, are 
required to detect it, and the term fixeJ may still be 
applied to the stars in contradistinction to such bodies as 
the planets. The largest proper motion found among 
the Northern stars is that of Groombridge, 1830, and 
this is only 7 7/ a year, at which rate it would make a 
complete tour of the heavens in 180,000 years if its 
motion continued uniform; the double star 61 Cygni 
has a proper motion of 5" a year, and many other stars 
have shown smaller, though still sensible motions, there 
being apparently every variety of motion, as there is 
every gradation of brightness. As in the case of 61 
Cygni, the radius of the earth's orbit at the distance 
of that star is //, 4, the star must annually move over 
about 12 times the distance of the sun from us, from 
which it follows that it is moving with four times the 
earth's velocity, or at the rate of about 70 miles a sec- 
ond. So many of the stars appear to have motions of 
their own, that it seems natural to suppose that our 
sun too may be in motion, carrying our earth and all 
the planets with him, one consequence of which would 
be to make all the stars appear to move in the opposite 
direction; and this furnishes a ready test of supposi- 
tion, for it is only necessary to see whether there i< 
any general drift of the stars which could be accounted 
for by a motion of the sun the opposite way. < her 
2,000 stars have been examined, and in the midst o£ 
much variety (as was to have been expected) there is 
found a general preponderance of motions away from 
the constellation Hercules, toward which the mid. 
therefore, appears to be moving. Although most of 
the stars move, as nearly as w r e can tell, uniformly in 
the same direction from year to year, there are a few 
exceptions, the most remarkable being Sirius, which is 



SIBIUS— BINARY STARS. 131 

found to describe an ellipse about a point at a mean ap- 
parent distance of 2|- " in something like 50 years, and 
Procyon, which revolves in 40 years nearly in a circle, 
having an apparent radius of 1 " . Such a motion would 
result from the attraction of another body, and in ac- 
cordance with this supposition a small star has been 
found some 10 " off, which revolves round Sirius some- 
what as the moon does round the earth(but at a distance 
greater than that of Neptune from the sun), whilst Sir- 
ius describes in space an ellipse about the center of 
gravity of the two. As the distance of these two is 
greater than that of Neptune from the sun, whilst their 
year is much less, the attracting force between them 
must be much greater, and by reasoning similar to that 
used in finding the sun's mass in terms of that of the 
earth (Chapter IV.), it follows that the attracting masses 
must be more than 20 times that of the sun and Nep- 
tune(the latter of which is comparatively small), and 
the center of gravity being twice as far from the com- 
panion as from Sirius, the mass of the latter must be 
about twice as great, or two-thirds of them. This can 
ouly be looked upon as a rough approximation, the 
numbers being extremely uncertain. In the case of 
Procyon, a similar companion star has been looked for 
but not found. 

The two stars above mentioned are rather peculiar 
examples of a very numerons class — stars revolving 
about each other. In a powerful telescope a large 
number of stars which are apparently single to the 
naked eye are seen to be composed of two, and some- 
times three or more stars very close together, a suffi- 
ciently remarkable circumstance considering how 
thinly the bright stars are scattered; and the interest 
in these objects has been enhanced by the discovery 
that in many cases each star is revolving round the 
other, forming what is called a binary system. From 
observations of the apparent direction of one star of 
such a system relatively to the other, combined with 
measures of the apparent distance between them, ex- 
tending over many years, the paths of a good many 



182 



BINARY STARS. 



have been determined; some of these are given in the 
following list, with the magnitudes of the two stars, 
their least and greatest distance apart, and the period 
in years: — 



Stab. 



Mag. 



Distance. 



Min. Max 



Per'd 

in 
Years 



Colors. 



£ Herculis 

?j Coronas 

£ Cancri j 

Sirhis 

t Ursse Majoris 
a Centauri... 
70 Ophiuchi. 

8 Cygni 

rf Cassiopeae. 
y Virginis .. 

Castor , 

61 Cygni 

y Leonis , 

£ 2 Lyrse , 

f 1 Lyrse , 



3, 6 

6, 6i 
6, 7 

1, 10 

4, 5£ 

1, 2 
4*. 7 
H, 9 
4, U 

4, 4 
3, 3£ 
5£, 6 

2, 4 

5, 6* 
5, 6£ 



// 

0-7 
0-7 
0-6 
5-2 
2-1 
1-5 
10 
2-4 
0-7 
2-6 
0-4 
4-7? 
15-5 
2-6 
2 



1-8 
1-2 
1-2 
5-8 

11-4 
3-5 

60 0: 
6-0 
2-9 

180 
6-8 
7-8 
? 
? 

5 





35 

40 

61 

700 

50 

60 

78 

93 

415 

180 

180 

60G? 

450? 

402 

1000 

2000 



Yellowish and orange. 
White and golden. 

1 Triple; all white. 

White. 
White. 

Yellow and violet. 

Yellow and sea green. 

Doubtful. 

White and pale yellow. 

White. 

Yellow. 

White. 

Yellow and ruddy. 



The parallax of some of the above stars has been 
determined, from which, as in the case of Sirius, the 
combined mass of the two stars of a Centauri has been 
found to be much greater than the sun's mass; of 61 
Cygni about }; and of 70 Ophiuchi about 3 times that 
of the sun. e 1 and e 2 Lyrse form a double binary sys- 
tem, visible to the naked eye, under exceptionable 
circumstances, as a very close double star near Vega, 
forming part of the pendant to the lozenge of Lyra; 
and C Cancri is a ternary system. 

Besides the binary stars, there are others between 
which a physical connection has not yet been estab- 
lished, and which may therefore possibly be composed 
of two stars only optically double, one star being 
nearly in a line with the other, but much further off. 
Some of these are most interesting objects from the 



DOUBLE STARS— SPECTRA OF STARS. 



133 



beautiful contrast of colors in the two stars. The fol- 
lowing may be selected as worth notice: — 



Star. 


Magni- 
tudes. 


Dis- 
tance. 




Colors. 




3,5 

3^,5 

3,6 

2K,9K 

4, 10, 7 


34 

3 

19 // 

10, 0.5 
12,42 


Double 
Double 
Double 


Golden and smalt blue. 


a Herculis 

£2 Bootis 


Orange and emerald green. 
Orange and blue. 


Polaris 

y Andromedee 
Of Orionis 


Double 'yellow and bluish. 
Triple Yellow and sea green. 
Triple i White, bluish, grape-red. 



From the evidence of the spectroscope it appears 
probable that difference of color in the stars corre- 
sponds in a general way to a difference of condition, 
the stars being divided broadly into three classes. 

1. White stars, like Vega, at a very high tempera- 
ture, and exhibiting a continuous spectrum with very 
fine absorption lines. 

2. Yellow stars (like our sun, Arcturus, Betelgeuse) 
at a lower temperature, showing strong absorption 
lines in a continuous spectrum. 

3. Red stars, in which the temperature is so low- 
that combination of the elements in their atmosphere 
takes place, and compound molecules are formed, 
showing a spectrum with broad absorption bands. 

In some of the stars of tho first and second classes 
the lines of hydrogen appear bright in the spectrum, 
indicating a huge conflagration of this gas, whilst with 
other stars, like our sun, the hydrogen is at a lower 
temperature, and absorbs more light from the pho- 
tosphere than it emits, causing dark lines in the 
spectrum. To such conflagrations the appearance of 
temporary stars, such as were seen in 1572, 160-4, 
1670, 1848, and 1866, appears to be due. On all these 
occasions bright stars burst suddenly on the view, 
and after a short time disappeared more or less com- 
pletely. Thus in 1866 a telescopic star in Corona sud- 
denly appeared of the second magnitude, fading away 



134 TEMPORARY AND VARIABLE STARS. 

in 12 days to the 8th or 9th magnitude; and the star 
of 1572 was even more remarkable, at one time sur- 
passing Jupiter in brightness. 

The temporary stars are only extreme instances 
of a much wider class, the variable stars, in which are 
found changes of all kinds, extending over periods 
ranging from nearly three days to an indefinite length, 
the variations of brightness recurring in some cases 
with the greatest regularity, whilst in others the 
changes seem to follow no definite law. Among the 
former are fi Persei (Algol), which is ordinarily of the 
second magnitude, but at intervals of 2 days 21 hours, 
diminishes to the fourth magnitude, and increases 
again to the second, all within the space of 7-J hours, 
A Tauri, which changes from 3^ to 4 magnitude in 4 
days, 8 Cephei from 3f to 5 magnitude in 5£ days, 
and (i Lyras fluctuating between 3^- to 4-j- magnitude 
twice in 12 days 21 hours. The star o Ceti (known as 
Mira) goes through its changes in about 11 months, 
but is very irregular as regards their extent, which 
sometimes ranges from brighter than the second mag- 
nitude to below the twelfth. The Southern star 
r] Argus is another remarkable variable, changing from 
first to sixth magnitude in an irregular period; a On- 
onis, a Herculis, a Hydrae, p Pegasi, rj Pegasi, and « 
Cassiopeae, are also irregularly variable, sometimes to 
the extent of half a magnitude or more, and many less 
conspicuous stars have been noted as variable. Nearlv 
all these stars are orange or red, and changes in color 
have in several cases been suspected, which would 
seem to show a change of temperature as they passed 
from a red to a white heat. Some of the double stars 
too are thought to have changed color, but accurate 
observations on this point are yet wanting, the eye 
alone being quite untrustworthy for absolute deter- 
minations of color. 

We saw that, when observations made at wide in- 
tervals came to be compared, many of the so-called 
fixed stars were found to be really in motion; but this 
is not the only startling result. The pole of the 



PBECESSIOX OF THE EQUINOXES. 135 

heavens is also found to be moving among the stars, 
very slowly, it is true, but still quite perceptibly. It 
will be remembered that all right ascensions and longi- 
tudes of stars are measured from the point where the 
sun crosses the equator, so that if the point shifts^ the 
right ascension and longitude of all objects will be 
altered, and this is found actually to be the case, the 
longitudes of all stars increasiug at the rate of about 
50" a year on account of a shift westward of the 
equator along the ecliptic, which is known as the pre- 
cession of the equinoxes. A clearer idea of this 
motion will be gained by considering the pole instead 
of the equator, which of course always moves with it. 
The pole of the heavens, then, is found to be at aii} r 
instant describing a very small arc of a circle about the 
pole of the ecliptic (which has itself a very small mo- 
tion) at a rate that would carry it completely round in a 
circle of about 23^-° radius in some 26,000 years. Now 
the pole of the heavens is nothing but the direction of 
the earth's axis, which it appears has not really a fixed 
direction in space, though in explaining the phenomena 
of the seasons it was unnecessary to take account of 
such a very small motion. Instead, then, of the earth's 
axis pointing always exactly in the same direction, it is 
circling round like a top, and from somewhat the same 
cause. The sun and moon pull the near part of the 
earth's equator (which bulges out) more than the other 
part (as in the case of the tides); but as the earth is 
spinning rapidly, the effect of this is not to bring the 
equator into the direction of the sun and moon, i. e., the 
ecliptic, but to make the earth's axis circle round the 
axis of the ecliptic, just as the gyroscope top hanging 
by a string on one side keeps a horizontal position, its 
axis turning round horizontally so long as it is spin- 
ning rapidly, though the attraction of gravity makes it 
hang straight down when at rest. This analogy will 
remove the difficulty of conceiving how such a seem- 
ingly paradoxical result could follow. In the case of 
the top, its weight tends to make it turn about a hori- 
zontal axis at right angles to its own (just as a hinged 



136 PRECESSION-NUTATION. 

flap would in falling), and the combination of this with 
fts P own rotation causes it to turn about an axis be- 
tween the two, thus making the axis, about wh.ch the 
I sp ns, mo've continually forward ; for there is * 
ev P ery instant a tendency (in consequence of the action 
of gravity) to turn about an axis a little in advance of 
thelctual'axis. Similarly the sun and moon tend to 
turn the earth about the intersection of the equator 
with the ecliptic as an axis, which combining^ with the 
actual rotation makes the earth spin about an axis a 
little toward the autumnal equinox so .that the ^pole o 
the heavens (being the direction of the earth s axis) 
moves a little towards the autumnal equinox thus de- 
Sing a very small arc of a circle about the pole of 
the ecliptic. Besides this regular recession, the earth ■ 
axl has P a wabbling motion depending on the incline- 
tion of the moon's orbit, causing the pole of the heavens 
to move really in a wavy line, each wave f, xtCnd '" g 
over nineteen years (lunar nutation); and there are, 
other irregularities modifying slightly though not de- 
stroying, ?he regular precession, which has earned the 
equfnofes through 3f/along the eclipse since the first 
catalogue of stars formed by Hipparchus in B. c. 1M, 
increafingthe longitudes of all stars by this amount. 
Thshasfntroduced some confusior .between i the ; con- 
stellations and the signs of the zodiac as . he t» 
parts into which it is divided, are called. In the time 
of Hipparchus the vernal equinox corresponded to the 
Commencement of the constellation A-s (reckoning 
from the west), and was hence called the first point oi 
Aries whilst the autumnal equinox was the first point 
of Libra, and the summer and winter solstices were in 
Cancer and Capricorn respectively; but ■ « '»■ 
eauinoxes have now moved to the constellations F.sces 
aSd Virgo, it is convenient to retain the old terms, 
and thus" a distinction has arisen between the constel- 
Tttns and the signs of the zodiac, the former Pre- 
serving their positions among the stars, whilst the la 
ter shift with the equinoxes, the sign Ar.es being now 
., he constellation Pisces, the sign Taurus uiAr.es, 



SIGNS OF THE ZODIAC. 137 

and so on. The practice, however, of referring the 
positions of the sun and planets to the signs of the 
zodiac has died out with the increase in the accuracy 
of observations, as the rough correspondence between 
the twelve signs and the twelve months of the year is 
no longer close enough even for the purposes of ordi- 
nary life. 



SUN AND MOON. 

The following table shows the principal periods of 
solar and lunar motion; with distances and diameters 
of the sun and moon: 

Sun's mean distance, miles 93,000,000 

Sun's diameter, miles 860,000 

Sidereal year, days 365*25636 

Tropical year, days 365*24220 

Or 11m 15s less than 365*4 days. 

Cycle of precession, years 25,800 

Moon's mean distance, miles '. 238.820 

least possible, miles 221,600 

" greatest possible, miles 253.000 

" diameter, miles 2.160 

" Sidereal period, days 27*32166 

" Synodical period, clays 29*5306 

" Anomalistic period, days 27*5546 

" Nodal period, days 27*21222 

Kevolution of lunar nodes, davs 6793*39 

" years 18*5997 

Saros (223 lunations), days 6585*3212 

Revolution of lunar perigee, davs 3232*5753 

years 8*8505 

Mass of earth, times that of Moon 81'5 



03 

H 

<! 

Hi 

o 

i— i 

Ph 

Eh 

O 

03 
Eh 

iJ 



1 ,- j fc iS -* 
1 .j\ £ °. n - °- ■"! 


•uoijuioh haSr o- . s; £ ^ S *" *" 

A 


•X^fsaaa 


P « • « 8 S * 8. *. 3 ■ 


^ 


,- ifi CO O O iO o 


1 


§ 


. £> <* d eo* © ^< co <n 


a 


h4 


k 5? 


fi 






*S 


L - - ir» o >--: cc i> 


o 




s 3 d "' S3 ^ s * '" 








p. 


o 


co 


S~ 00 




T r_i^ 


— ~. © ■- N H e« © 
=5 o d rH d «-< o T'-" 


- ~ = 1 £ 


.5 = =w 


G=. 1 


°S| 


CO rH © © £ t- 
v . © CN = t-~ <-< "^ "* ^ 




■ £^ '.-J O rH rl CM d rl 






^o3 






o8«d 

OQ « 

s> a 


: ^ ^ ^ -" -" 

: - ;i So o oo o - - 


£.S 


Sx 




Period 

in 
Solar 
Uavs. 


• 00 ifi & fc w ?? V S 

! °° a » s g g | | 




gui^. i 1 


: - £ § 8 8 S ? «- 

• d © o -' "»" d c^ © 


*s*l 


H 




istance 

an (in 

Kiirth 

Dista 


IS 


. i» » l-- o - f ^ P" 5S 
! » " S 8 5 d © S 

= 00- - « S 


n*>- 


5 




1 


': >. 








: o 

■ z 


ft 


i iiii 


.- - £ -r 

=■ § £ r 
I 5 «S5 & * 


•joquiXs 


Gxhcm-Q^o^^S 3 ^ 



2. £ s-r 



GO 


Sj 


S3 


ffi 


g 


hQ 






O 


s 


s, 


»d 


e+- 





fi 




3- X 






O 

X 

ra 


3 
— . 




ro 


ro 






vj 




<J 


- r J 


no 


— 


L_| 
















~ 




< 


jq 




jf{. 




J- 


- 


Z 


- 


- 



a 


&. 


_*. 








go 3" 


o 


cc 


3 C 


rt 


C/J 


© c 


— 
CD 




2 o 





m 



s-5 ° C- 



5 © •— ■ 
' 5 =7q 



s CD » C go tf- -CD -<=3»-i 3 

£fc2 srEtaJ 5 - - 5 3 ^ 



~ ~ ~ - 



b^COtoOCrfi-bsrf^obibiOC 



mmOmhOmmoOO 

h* oo bso^aepeobobcca be 



Cn 4^ p> O pi OS p» 4s» pr p» *>• 
J- 1 -J 00 w"< C© tw ^3 GC £H -1 J-* 



^ w ^ — ' - ■ — > i— — «vi ^— ,_, 



tOM tOCOtO)— ' l— ' I— ' ic 

c tc i" 1 c: - ■*» -^ <i — c; i; 



x x x x x x x x x x x 

gc -a ii -a x in -a -3 -j -1 00 

p OOpi H-p _CO <lp p'p^ 

3.f ^ppf«^4^1° 



CD 2. 

S3 O 



Q 

CD 



LITERATURE MANUALS. 

18mo.,Cloth,40 Cents. 



ENGLISH LITERATURE.-By Stoppord Brooke, 
M.A. American revised edition, brought to date 
by Frank Gilbert, A. M., author of " The World, 
Historical and Actual." 

AMERICAN LITERATURE.— By Frank Gil 

BERT, A.M. 

GREEK LITERATURE.— By R. 0. Jebb Amer- 
ican enlarged edition, by Frank Gilbert, A.M. 

ROMAN LITERATURE.— By Frank Gilbert, 
A.M. 

SCIENC E MAN UALS. 

MANUAL OF ASTRONOMY.— By W. H. Christie, 
M.A., of the Royal Observatory, Greenwich. Amer- 
ican edition revised by Prof. Colbert, late of 
Dearborn University, Chicago. 

MANUAL OF PHYSIOLOGY.— Introduction and 
Revision by Sarah Hackett Stevenson, M. D., 
late Professor in the Women's Medical College, of 
Chicago. 

MANUAL OF GEOLOGY.— By A. Geikie. With 
an introduction by Alexander Winchell, of 
University of Michigan. 



HISTORY MANUALS. 

GREEK HISTORY.— By C. A. Fyffe, of Univer- 
sity College, Oxford. American edition, by Frank 
Gilbert, A.M. 

ROMAN HISTORY.— By M. Creighton, of Merton 
College, Oxford. American edition by Frank Gil- 
bert, A.M. 

OTHER MANUALS IN PREPARATION. 



COLBERT'S FIXED STARS. 



Maps For Out-door Study of the Heavens. 



Adapted to use in schools, or without a teacher. Contains 

12 maps, showing the principal stars in all the constellations ; 

each outlined similar to plan in frontispiece of this 

work. Also, tables for rising and setting, etc. 

Price, SO Cents, by Mail. 



COLBERT'S MATHEMATICAL TABLES 

To Four Places (and a fraction). 

They suit every need of the class-room. The use of loga- 
rithms can he taught just as well with tables to four places, as 
if six or seven places be employed ; and the work is much 
easier. This little book also presents the convenience of being 
portable, and separate from the text-book. 

Price, 40 Cents, by Mail. 

Wm. Habkness, of TJ. S. N Observatory, at Washington, 
and Professor of Mathematics in the United States Navy, ivrites, 
Nov. 25, 1881 : 

"I beg to assure you that it will be very convenient to me, 
because it is the most portable collection of four-figure loga- 
rithms that I know of. If the public realized the time-saving 
properties of such tables, you wo aid scarcely be able to supply 
the demand for them." 



FOB SALE BY 

FAIRBANKS, PALMER & CO, 



THE WORLD: 

HISTORICAL AND ACTUAL. 

WHAT HAS BEEN AND WHAT NOW IS. 

OUK GIOBIC IN ITS RELATIONS TO OTHER WORLDS, AND BEPOBK MAN— 

ANCIENT NATIONS IN THE ORDER OF THEIR ANTIQUITY— 

THE MlDD. E AGES AND THEIR DARKNESS— 

THE PRESF.NT PEOPLES OF THE EARTH IN THEIR GRADUAL EMERGENCE 

FROM BARB \ RTSM INTO THE SUNLIGHT OF TO-DAY, AND AS THEY 

NOW STAND UPON THE PLANE OF CIVILIZATION J 

TOGETHER WITH 

USEFUL AND INSTRUCTIVE CHARTS. 

REFERENCE TABLES OF HISTORY, FINANCE, COMMERCE AND 
LITERATURE, FROM B. C. 1500 TO THE PRESENT TIME. 



ONE LARGE QUARTO VOLUME. 

718 B^G-JUS. 

NEARLY ONE THOUSAND ILLUSTRATIONS. 



By FRANK GILBERT, A. M., 

Late Assistant Treasurer, U. S. at ' ticago, and Associate Edi'or of C'dcaqo 
Journa ; Author of the Manual of American Literature. 



THE WORLD. HISTORICAL AND ACTUAL, gives with accuracy 
-.ne past and present of all the nations and peoples of the world aneii nt 
and modern. Each is traced in its development according to it- ordc . 
importanr-e and in f erest. Its scope may be interred from the above title 
It is published in one large, royal quarto volume of 718 pages, printed 
from clear new type, on fine, tinted, heavy, super-calendered paper, 
made expr* sslv for this book, with nearly 1,000 illustrations, and bound 
in the most substantial and elegant manner, side stamps in black and 
gold, of icautiful designs, and fu nished to subscribers at the following 
prices : 

In English Silk Cloth, Bach and Side in Black and 

Gtd-i, Sprinkled Edges, - - - $ 6 SO 

In Englis'i Cloh, Back and Sides in B'ack and Gold, 

Gilt Edges, - - - 7 SO 

In Libra in/ Stt/le, Fall leather, Marbled Edges, - 7 SO 

In American Russia, Pr-sentation Edition, Gilt Edges, lO OO 

SOLD OlSTLY BY SUBSCRIPTION. 



Active, Energetic Agents Wanted, 



FAIRBANKS, PALMER & 00., 



PUBLISHERS, 



680 and 682 Broadway, New York. 

203 and 205 Wabash Av., Chicago, DL 



GASKELL'S 

Compendium of Forms. 

Educational, Social, Legal and Commercial. 

One Large, Elegantly Illustrated Quarto Volume. 

BY PROF. G. A. GASKELL, 

— EMBRACING 

A COMPLETE SELF-TEACHING COURSE IN PENMANSHIP AND BOOK-KEEPING, 

ALSO, SHORTHAND, AND AID TO ENGLISH COMPOSITION, INCLUDING 

ORTHOGRAPHY, CAPITAL LETTERS, PUNCTUATION COMPOSITION, 

ELOCUTION, ORATORY, RHETORIC, LETTER-WRITING IN 

ALL ITS FORMS: THE LAWS AND BY-LAWS OF 

SOCIAL ETIQUETTE ; BUSINESS, LAW, 

AND COMMERCIAL FORMS. 

Dictionary of Legal and Commercial Terms. 

20,000 SYNONYMS, 

ABBREVIATIONS, FOREIGN PHRASES, POETRY, Etc. 

Also, a Manual of Agriculture ard Mechanics ; with a Complete Guide to 
Parlimentary Practice, Rules of Order for Deliberative Assem- 
blies, Organization and Conduct of Meetings, etc.; Game 
Laws of the United States and Provinces. 



This book has just been issued, and embraces a great many more subjects 
than any similar work heretofore offered, and in all cases presents the latest re- 
searches in its various branches. A wide scope of information, arranged in the 
most concise manner consistent with ease and absolute clearness, and presented 
in the highest artistic dress, is here offered to the public, with the conviction that 
the aim has been attained to prepare such a work that the judament of the care- 
ful critic will be that none wuo desire the BEST will be without it. 

Description audi Prices. 

Gaskell's Compendium of Forms is published in one large, royal quarto 
volume, printed from clear, new type, on fine, tinted, heavy, extra super calen- 
dered paper, made expressly for this book, finely illustrated, and bound in the 
most substantial and elegant manner, side stamps in black and gold, of beautiful 
designs, and furnished to subscribers at the following prices : 
In English Silk. Cloth Back and Side, in Black and Gold, Sprinkled Edges, $ 6.00 

In Lihrarv Stvle, Full Leather, Marbled Edges, 7.00 

In American Russia. Gilt Edges, 8.50 

In Full Turkey Morocco Antique, Presentation Edition, Gilt Edges, - 11.00 

The publishers guarantee the book to correspond in every respect 
with samp'.e copy, and unless it does, those who orde the work will be 
under no obligations to take it. Sold only by subscription 

Active, Energetic Agents Wanted. 

FAIRBANKS, PALMER & CO., Publishers, 

680 & 682 Ttrnaflivav, 203 A 205 Wabnsh Ave,, 

NEW YOItK CHICAGO. 



